International Conference on Mathematical Methods
in Physics

In memory of Professor Ahmed Intissar

Book of abstracts
1-5 April 2019 Marrakech
MoroccoICMMP 2019

In memory of Ahmed Intissar

The conference venue is
Ryad Mogador Kasba Hotel2

38

Contents

Contents

3

In Memory of Ahmed Intissar

4

Teams

5

List of registered participants

6

Harmonic analysis, representation theory and quantization

9

Clifford algebras, Clifford analysis and applications

14

Coherent states & wavelets

15

q-deformation, Hopf algebras and quantum groups

19

Geometric mechanics, non-commutative geometry and symmetry20

Orthogonal Polynomials, special functions, exact solvable systems, non-linear systems

23

Spectral theory and quantum systems, quantum information

26

Posters31

Schedule of talks

34

Acknowledgments

37

3

38

Professor Ahmed Intissar (1951-2017)

At the Faculty of Sciences and Technics
Béni Mellal, 1995

After obtaining his PhD at the Massachusetts Institute of Technology(MIT) in 1985, Professor Ahmed Intissar returned to his native Morocco.
Over the years, he supervised several
PhD thesis, creating a school of mathematics which is worldwide recognized for fundamental contributions
both in mathematics and mathematical physics. His students, friends
and collaborators will always remember him for his teaching, his science and his charismatic personality.

438

TeamsOrganizing committee
Abdelhamid Boussejra, Ibn Tofail University, Morocco
Paula Cerejeiras, Aveiro University, Portugal
Allal Ghanmi, Mohammed V University, Morocco
Yassine Hassouni, Mohammed V University, Morocco
Zouhaïr Mouayn (Chair), Sultan Moulay Slimane University, Morocco
Hassan Sami, Hassan II University, Morocco

Scientific committee
Abdelhamid Boussejra, Ibn Tofail University, MoroccoHans G. Feichtinger, Vienna University, Austria
Jean P. Gazeau, Paris Diderot University, France
Zouhaïr Mouayn, Sultan Moulay Slimane University, Morocco
Ablamowicz Rafal, Tennessee Technology University, USA

Student Team
Khalid Ahbli, Ibn Zohr University, Morocco
Othmane El Moize, Ibn Tofail University, Morocco
Mohammed Mahboubi, Ibn Tofail University, Morocco
Ismail Ouaadi, Mohammed V University, Morocco
Ghayth Ouirdani, Sultan Moulay Slimane University, Morocco

Proceeding
The best papers presented at the conference and thematically connected with Clifford algebras or Clifford analysis and applications, Hopf algebras and quantum groups, geometric mechanics and symmetry, Clifford wavelets, etc will be submitted for
publication in Advances of Applied Clifford Algebras (AACA) https://www.springer.com/birkhauser/physics/journal/6. The best
papers related to Harmonic analysis, representation theory and quantization, Coherent states & wavelets, q-deformation, Orthogonal Polynomials and special functions, exact solvable systems, Spectral theory and quantum systems, will be submitted for
publication in Complex Analysis and Operator Theory (CAOT) https://www.springer.com/birkhauser/mathematics/journal/11785.

538

List of registered participants

A

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Full Name
S. Abumaryam
M. A. Abdelmoumene
Luís Daniel Abreu
Mariano A del Olmo
Khalid Ahbli
Hélène Airault
M. Ait Ben Haddou
Abdessamad Ait Brahim
Pedro Alberto
Mohamed Amazioug
Tarik Amtout
Sama Arjika
Azzouz Awane
Fida Bahba
Fabio Bagarello
Ali Baklouti
Peter Balazs
Edwin Beggs
Abdessamad Belfakir
Abdelhadi Benahmadi
Abdessalem Benammar
Jasel Berra-Montiel
Christian Berg
Mohamed Berkani
Stefan Berceanu
Djahida Bouchefra
Abdelhamid Boussejra
Danail Brezov
Paula Cerejeiras
A.Benaissa Cherif
Evaldo Curado
Briceyda B. Delgado
A. S. Diallo
Kamal Diki
Amal El Hamyani
Othmane El Moize
Omar El-Fallah
Omar El Fourchi
Fouzia El Wassouli
Abderrahman Essadiq
Pavel Exner
Said Fahlaoui
Jacques Faraut

Affiliation and Email
Sirte Univ., LIBYA, Souad22008@yahoo.com
Brothers Mentouri Constantine 1 Univ., ALGERIA, Adib.m.abdelmoumene@gmail.com
Austrian Academy of Sciences, AUSTRIA, labreu@kfs.oeaw.ac.at
Valladoli Univ., SPAIN, olmo@fta.uva.es
Ibn Zohr Univ., MOROCCO, ahbli.khalid@gmail.com
Picardie Jules Verne Univ., FRANCE, Helene.airault@u-picardie.fr
Moulay Ismail Univ., MOROCCO, maitbenha@gmail.com
Sultan Moulay Slimane Univ., MOROCCO, mouayn@gmail.com
Coimbra Univ., PORTUGAL, lena@mat.uc.pt
EPTHE, Ibn Zohr University, Agadir, MOROCCO, amazioug@gmail.com
Faculty of Sciences and Techniques Tangier, MOROCCO, tareqfstt@gmail.com
Agadez Univ., NIGER rjksama2008@gmail.com
Hassan II Univ. , MOROCCO, a.awane@yahoo.fr
Monastir Univ., TUNISIA, fidabahba@gmail.com
Palermo Univ., ITALY, fabio.bagarello@unipa.it
Sfax Univ., TUNISIA Ali.Baklouti@fss.usf.tn
Austrian Academy of Sciences, AUSTRIA, peter.balazs@oeaw.ac.at
Swansea Univ., WALES, e.j.beggs@swansea.ac.uk
Faculté des sciences -Rabat, MOROCCO, abdessamad.belfakir@um5s.net.ma
Mohammed V Univ., MOROCCO, abdelhadi.benahmadi@gmail.com
Research Center in Industrial Technologies (CRTI), ALGERIA, Abs_benammar@yahoo.fr
Universidad Autonoma de San Luis Potosi, MEXICO, jasel.berra@uaslp.mx
Copenhagen Univ., DENMARK, berg@math.ku.dk
Mohammed I Univ., MOROCCO, berkanimo@aim.com
National
InstituteforPhysics
andNuclearEngineering,
ROMANIA,
Berceanu@theory.nipne.ro
Melilab –Mila. ALGERIA, Djahida.bouchefra@gmail.com
Ibn Tofail Univ., MOROCCO, a.boussejra@gmail.com
Architecture, Civil Engineering and Geodesy Univ., BULGARIA, danail.brezov@gmail.com
Aveiro Univ., PORTUGAL, pceres@ua.pt
Science & Technologu Univ., ALGERIA, Amine.banche@gmail.com
Centro Brasileiro de Pesquisas Físicas, BRAZIL, evaldo@cbpf.br
Southern Federal Univ., RUSSIA, briceydadelgado@gmail.com
Alioune Diop de Bambey Univ., SENEGAL, Abdoulsalam.diallo@uadb.edu.sn
Politecnico di Milano, ITALY, kamal.diki@gmail.com
Mohammed V Univ., MOROCCO, amalelhamyani@gmail.com
Ibn Tofail Univ. MOROCCO, elmoize.othmane@gmail.com
Mohammed V Univ., MOROCCO, elfallah@fsr.ac.ma
CRMEF Rabat, MOROCCO, elfourchi@gmail.com
Ibn Tofail Univ. , MOROCCO, elwassouli@gmail.com
Ibn Tofail Univ., MOROCCO, aessadiq@yahoo.fr
Charles Univ., CZECH REPUBLIC, exner@ ujf.cas.cz
Moulay Ismail Univ., MOROCCO, saidfahlaoui@gmail.com
Pierre & Marie Curie Univ., FRANCE, jacques.faraut@imj-prg.fr
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In memory of Ahmed Intissar

Full Name
Nelson Faustino
Hans G. Feichtinger
Milton d. S. FerreiraFrancesco Gargano
Jean P. Gazeau
Allal Ghanmi
Ali Hafidi
Iness Haouala
Yassin Hassouni
Aziz Hilali
Noureddine Imesmad
Vladimir Jacimovic
Igor Kanatchikov
Tomas Kalvoda
Patrick Kayupe Kikodio
Uwe Kähler
Vladimir V. Kisil
Khalid Koufany
Abdelhak Kouraich
Fatima Zohra Ladrani
Jerzy Lukierski
M. Mahboubi
A. Makhlouf
Amel Mazouz
Mostafa Mbekhta
Alberto Molgado
Issam Mouayn
Zouhaïr Mouayn
Z. Mouhcine
Samuel Nuugulu
Anatol Odzijewicz
Youssef Omari
Ismail Ouaadi
Achraf Ouald Chaib
Ghayth Ouirdani
Nadia Ourchane
Lassi J. Päivärinta
Georgi Raikov
Hassan Sami
Nobukazu Shimeno
Tomoyuki Shirai
Dmitry Shirokov
Mohamed Sifi
Aneta Sliżewska
Yahyeh SouleimanTaoufiq Tahani
S. Tremblay
Apostol Vourdas
H. A. Yamani
Slimane Zaiem
Ahmed I. Zayed
Ahmed Zeghal
Mohammed Ziyat

Affiliation and EmailFederal do ABC Univ., BRAZIL, nelson.faustino@ufabc.edu.br
Vienna Univ., AUSTRIA, hans.feichtinger@univie.ac.at
Polytechnic Institute of Leiria, PORTUGAL, Milton.ferreira@ipleiria.pt
Palermo Univ., ITALY, Francesco.gargano@unipa.it
Paris Diderot Univ., FRANCE, gazeau@apc.univ-paris7.fr
Mohammed V Univ., MOROCCO, allalghanmi@gmail.com
Moulay Ismail Univ., MOROCCO, Hafidiali28@gmail.com
ESSTHS, TUNISIA, Iness.haouala@yahoo.fr
Mohammed V Univ., MOROCCO, y-hassou@fsr.ac.ma
INPT, MOROCCO, hilali@inpt.ac.ma
Ibn Tofail Univ., MOROCCO, Imesmad75@gmail.com
Montenegro Univ., MONTENEGRO, vladimir@jacimovic.me
U. St Andrews, Scotland and Natl. Quantum Information Center, POLAND, ik25@standrews.ac.uk
Czech Technical Univ., CZECH REPUBLIC, Tomas.kalvoda@fit.cvut.cz
Ibn Tofail Univ., MOROCCO, kayupepatrick@gmail.com
Aveiro Univ., PORTUGAL, ukaehler@ua.pt
Leeds Univ., UK, kisilv@maths.leeds.ac.uk
Lorraine-Nancy Univ., FRANCE, Khalid.Koufany@univ-lorraine.fr
MOROCCO, akouraich@yahoo.fr
Higher Normal School of Oran, ALGERIA, f.z.ladrani@gmail.com
Wroclaw Univ., POLAND, Jerzy.lukierski@ift.uni.wroc.pl
Ibn Tofail Univ., MOROCCO, Mohammedmahboubi04@gmail.com
Haute Alsace Univ., FRANCE, abdenacer.makhlouf@uha.fr
Djillali Bounaam Univ., ALGERIA, Mazouz.amel@yahoo.fr
Lille Univ., FRANCE, mostafa.mbekhta@univ-lille.fr
Autonoma de San Luis Potosi Univ., MEXICO, Alberto.molgado@uaslp.mx
SCR & CARC, MOROCCO, imouayn@scrmaroc.com
Sultan Moulay Slimane Univ., MOROCCO, mouayn@gmail.com
Mohammed V Univ., MOROCCO, zakariyaemouhcine@gmail.com
Namibia Univ., NAMIBIA, snuugulu@unam.na
Institute of Mathematics, POLAND, aodzijew@uwb.edu.pl
Faculté des sciences de Rabat, MOROCCO, omariysf@gmail.com
Mohammed V Univ., MOROCCO, ismail.ouaadi@gmail.com
Ibn Tofail Univ. MOROCCO, achrafoualdchaib@gmail.com
Sultan My. Slimane Univ., MOROCCO, ghaythouirdani@gmail.com
Ibn Tofail Univ., MOROCCO, nadia.ourchane20@gmail.com
Tallinn Univ. of technology, ESTONIA, Lassi.paivarinta@ttu.ee
Pontificia Catolica Univ., CHILE, graikov@mat.uc.cl
Hassan II University, MOROCCO, samydavis_743@gmail.com
Kwansei Gakuin Univ., JAPAN shimeno@kwansei.ac.jp
Kyushu Univ., JAPAN, shirai@imi.kyushu-u.ac.jp
National Research Univ., RUSSIA, dm.shirokov@gmail.com
Tunis El Manar Univ., TUNISIA, mohamed.sifi@fst.utm.tn
Institute of Mathematics Bialystok Univ., POLAND, anetasl@uwb.edu.pl
Djibouti Univ., DJIBOUTI, yahyehlakios@gmail.com
Lille 1 Univ., FRANCE, Taoufiq.Tahani@math.univ-lille1.fr
Québec Univ ., CANADA, sebastien.tremblay@uqtr.ca
Bradford Univ., UK, a.vourdas@bradford.ac.uk
King Abdullah City for Atomic and Renewable Energy, SAUDI ARABIA, haydara@sbm.net.sa
Batna 1 Univ., ALGERIA, zaim69slimane@yahoo.com
DePaul Univ., USA, azayed@depaul.edu
Sultan My. Slimane Univ., MOROCCO, zeghal@yahoo.com
Mohammed V Univ., MOROCCO, Ziyatmohammed17@gmail.com
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In memory of Ahmed Intissar

Abstracts

838

Harmonic analysis, representation theory andquantization
Plenary talks
Luís D. Abreu (Austria)
Planar electrostatics in higher Landau levels
Abstract. The beta-Weyl-Heisenberg ensemble will be suggested as a new Ansatz for electrostatics without confining potential, with the aim of overcoming the radial restrictions imposed on the confining potential by the structure of the Landau
equation with a constant magnetic field. Particular cases include the 2D Coulomb gas model, the Ginibre ensembles, thepolyanalytic ensembles, Laughlin’s wave function, its lift to higher Landau levels and the Weyl-Heisenberg ensemble, recently
introduced and studied in collaboration with Gröchenig, Pereira, Romero and Torquato. Further developments will be presented,
based on joint work with Haimi and Luef and suggested by work of Duncan Haldane and the school of Ahmed Intissar.
Hélène Airault (France)
Matrix operators on symmetric Kaehler domains
Abstract. We show how to obtain the Laplacian and Ornstein-Uhlenbeck operators on some particular submanifolds of the
Cartan domains II and III. This work extends the papers by Airault (Bull. Sci. math. 2012) and by Airault-Bouusejra (Bull. Sci.
math. 2013)
Ali Baklouti (Tunisia)
Harmonic Analysis around monomial representations of exponential solvable Lie groups
Abstract. We discuss in this talk some problems related to a monomial representation τ = indG
H χ where G denotes
an exponential solvable Lie group, H an analytic subgroup of G and χ a unitary character of H. The goal is to
study The Plancherel formula and the algebra of G-invariant differential operators on the homogeneous space G/H.
Stefan Berceanu (Romania)
Differential geometry on homogeneous spaces attached to the Jacobi group
Abstract. The semidrect product GJn of the (2n + 1)-dimensional Heisenberg group with the symplectic group of adequate
dimension is known in Mathematics as the Jacobi group. The Jacobi group has many applications in Physics, beeng the groupresponsable for the squeezed states in quantum optics. Using the coherent state approach, we have determined the Kähler
potential on the Siegel Jacobi ball and Siegel Jacobi upper half plane, which are homogeneous spaces attached to the Jacobi
group, extending the results of Erich Kähler in the case n = 1. The invariant metric on the Kähler manifolds Siegel-Jacobi
ball and Siegel-Jacobi upper half plane are balanced. Considering the real Jacobi group GJ1 (R) as subgroup of submatrices ofSp(2, R), we study metric on the Siegel-Jacobi spaces invariant to the action of the Jacobi group. We calculate invariant metricon the 5-dimensional extended Siegel-Jacobi upper half plane.

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ICMMP 2019

In memory of Ahmed Intissar

Omar El-Fallah (Morocco)
Estimates of the singular values of Hankel operators on Bergman spaces
Abstract. Let D be a the unit disc of the complex plane and let A2ω be the Bergman space defined byZ
A2ω := {f ∈ Hol(D) :|f (z)|2 ω(z)dA(z)},Ω

where ω : Ω → (0, +∞) is a continuous weight.
Let P the orthogonal projection from L2 (ωdA) onto A2ω . The Hankel operator associated with an anti-analytic symbol b̄ isgiven byHb̄ f = b̄f − P b̄f, f ∈ A2ω .
In this talk we will discuss the boundedness, compactness of Hb̄ . We will also give some estimates of the singular values ofHb̄ . Other classes of operators will also be considered.
Khalid Koufany (France)
Conformally covariant bi-differential operators for differential forms
Abstract. The Rankin-Cohen bidifferential operators have attracted considerable attention in recent years particularly becauseof their applications to various areas including the theory of modular forms, covariant quantization, ring structures on
representations spaces, branching law, ...
From the view point of representation theory the Rankin-Cohen operators are intertwiners in the branching law for thetensor product of two holomorphic discrete series representations of SL(2, R) : they give explicit intertwining operators fromthe tensor product of a given pair of irreducible representations into another irreducible representation (of higher weight).
In the first part of this talk I will explain the construction of a generalization of Rankin-Cohen bidifferential operators acting
on C ∞ (V ), which are covariant under the conformal group G of a simple real Jordan algebra V (see [1]).
In the second part I will construct these operators, replacing V by Rn , the groupe G by SO0 (1, n + 1) viewed as the conformalgroup of Rn , and C ∞ (V ) by differential forms (see [2]).
If time permits, I will also discuss the case of spinors ([3]).
References
1 S. Ben Said, J.-L. Clerc, K. Koufany. Conformally covariant bi-differential operators on a simple real Jordan algebra. International Mathematics
Research Notices, May 2018, https://doi.org/10.1093/imrn/rny082.
2 S. Ben Said, J.-L. Clerc, K. Koufany. Conformally covariant bi-differential operators for differential forms. To appear in Communication in Mathematical
Physics. arXiv:1809.06290.
3 S. Ben Said, J.-L. Clerc, K. Koufany. Conformally covariant bi-differential operators for spinros. In preparation.

Nobukazu Shimeno (Japan)
Matrix valued spherical functions on real semisimple Lie groups
Abstract. Let G = KAN be a connected real semisimple Lie group of finite center. We define a notion of “minuscule K-types”,
which is a generalization of the notion of fine K-types for real split Lie groups due to Vogan and the notion of minuscule
K-types for complex Lie groups. Under some additional conditions, there exists a first order invariant differential operatorson the homogeneous vector bundle over G/K associated with a minuscule K-type. Moreover, the matrix valued elementary
spherical functions on G for such a minuscule K-type can be expressed explicitly by Opdam’s non-symmetric hypergeometricfunctions associated with the restricted root system of G/K. We also give some applications in harmonic analyisis for sphericalfunctions.
This talk is based on joint work with Hiroshi Oda.

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ICMMP 2019

In memory of Ahmed Intissar

Ahmed I. Zayed (USA)Sampling on a disc for a class of linear canonical transforms

Abstract. Sampling of bandlimited functions in different integral transform domains, such as Fourier, Hankel, and Legendre transforms, has been studied extensively either directly or indirectly through the initial-value problems which
the kernels of the transforms satisfy. Some of these transforms have been extended to higher dimensions and more
recently they have been extended to fractional orders. Sampling in higher dimensions is challenging because the distribution of the sampling points depend on the kernel of the transform as well as on the shape of the domain on
which the transform is restricted. In this talk we will present a sampling theorem for functions that are bandlimited
to a disc in the linear canonical transform domain, which includes the fractional Fourier transform as a special case.

Contributed talks
Jasel Berra-Montiel (Mexico)
Towards a representation of Loop Quantum Gravity in the Deformation Quantization approach
Abstract. We analyze the loop representation of quantum mechanics within the deformation quantization formalism. In
particular, we construct the Wigner function and the star-product as a distributional limit of the Schrödinger representation for
the Weyl algebra and we observe that this limit agrees with the Wigner function for Loop Quantum Cosmology. Finally, within
our framework, we also derive a generalized uncertainty principle which is consistent to the ones usually obtained in theories
assuming a fundamental minimal length in their formulation.
Fouzia El Wassouli (Morocco)
Wigner transform on line bundle on bonded symmetric spaces
Abstract. We generalized the Wigner transform on line bundle on bonded symmetric spaces. We also proved some it’s
properties and relations.
Milton dos Santos Ferreira (Portugal)
Gyroharmonic analysis and the continuous wavelet transform on the ball
Abstract. I will present the main results concerning gyroharmonic analysis on the ball with an arbitrary radius. Starting from the gyrogroup structure of the ball we construct the main tools of harmonic analysis on the ball: the unitarytranslation operator, the generalized eigenfunctions of the Laplace-Beltrami operator and the generalized Fourier-Helgason
transform for the ball with hyperbolic geometry enclosed. With these tools in hand, we properly define a continuous
wavelet transform on the ball by incorporating a class of radial relativistic operators together with motions on the ballgiven by Möbius transformations. We study the admissibility condition for this transform in order to have admissible
wavelets and we give examples of admissible hyperbolic wavelets. The resulting wavelet transform is invertible whenever
the mother wavelet satisfies a particular admissibility condition, which turns out to be a zero-mean condition. For large
radiuses of the ball the continuous wavelet transform on the ball matches the usual continuous wavelet transform in Rn .
Noureddine Imesmade (Morocco)
A characterization of the L2 -range of the Poisson transform on homogeneous line bundles over the matrix ball
Abstract. Let X = G/K be a Riemannian symetric space of the noncompact type. In [1] Kaizuka solved the Strichartz
conjecture on an image characterization for the Poisson transform Pλ on L2 -functions on the Furstenberg boundary, withregular parameter λ. In this talk we extend the above result to the case of a class of homogeneous line bundles over thehermitian symmetric space SU (n, n)/S(U (n) × U (n)). This talk is based on a joint work with A. Boussejra.
References
1 A characterization of the L2 -range of the Poisson transform related to Strichartz conjecture on symmetric spaces of noncompact type, Adv. Math
303 (2016), 464-501.

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ICMMP 2019

In memory of Ahmed Intissar

Youssef Omari (Morocco)
Riesz bases of reproducing kernels in small Fock spaces
Abstract. We give a complete characterization of Riesz bases of normalized reproducing kernels in the small Fock space Fϕ2 , thespace of entire functions f such that f e−ϕ ∈ L2 (C), where ϕ(z) = (log+ |z|)β+1 , 0 < β ≤ 1. The first results on this subject
are due to Borichev-Lyubarskii who showed that ϕ with β = 1 is the biggest weight for which the corresponding Fock space
admits Riesz bases of reproducing kernels. Later, such bases was characterized in Baranov et al. [1] for the case when β = 1.
The present paper answers a question in [1] by extending their results for all parameters β ∈ (0, 1). Our results are analogues
to those obtained for the case β = 1 and those proved for Riesz bases of complex exponentials for the Paley-Wiener spaces.
We also obtain a description of complete interpolating sequences in small Fock spaces with associated uniform norm. We
characterize also complete interpolating sequences for the Fock spaces Fϕp , 1 6 p < ∞, where ϕ(z) = α(log+ |z|)2 , α > 0.
Our results are analogue to the classical Kadets-Ingham’s 1/4-Theorem on perturbation of Riesz bases of complex exponentials
and they answers questions asked in [1].
References
1 A. Baranov, A. Dumont, A. Hartmann, K. Kellay. Sampling, interpolation and Riesz Bases in small Fock spaces. J. Math. Pures Appl. (9) 103 (2015),
no. 6, 1358–1389.
2 A. Borichev and Yu. Lyubarskii, Riesz Bases of reproducing kernels in Fock type spaces, J. Inst. Math. Jussieu 9 (2010), no. 3, 449–461.

Achraf Ouald Chaib (Morocco)
The Poisson transform on homogeneous vector bundles over Sp(n, 1)/Sp(n) × Sp(1)
Abstract. In this talk I will give an image characterization of the Poisson transform on L2 -sections of a class of homogeneous
vector bundles associated to finite irreducible representations of Sp(n) × Sp(1) which are trivial on Sp(n). This extends
previous results in [1] and [2] to the case of homogeneous vector bundle case over Sp(n, 1)/Sp(n) × Sp(1). This talk is basedon a joint work with A. Boussejra.
References
1 A. Boussejra, A. Intissar, L2 -concrete Spectral Analysis of the Invariant Laplacian in the Unit Complex Ball. J. Funct. Anal. 160 (1998), 115-140.
2 A characterization of the L2 -range of the Poisson transform related to Strichartz conjecture on symmetric spaces of noncompact type, Adv. Math
303 (2016), 464-501.

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In memory of Ahmed Intissar

Nadia Ourchane (Morocco)
Characterization of the Lp -range of the Poisson transform on the Octonionic Hyperbolic plane
Abstract. In this talk, I will give a necessary and sufficient condition on eigenfunctions F of the Laplace-Beltrami operator
on the octonionic hyperbolic plane B(O2 ) = F4(−20) /Spin(9) with eigenvalue −(λ2 + ρ2 ) (λ a real number )to have an
Lp -Poisson integral representations on the boundary ∂B(O2 ), for p ∈]1, ∞[ . Namely, F = Pλ f for some f ∈ Lp ∂B(O2 ) if
and only if it satisfies the following growth condition of Hardy-type:2

kF k∗,p := sup (1 − r )

−ρ
2

Z

!1

p

p

|F (rθ)| dθ< ∞.

∂B(O2 )

0≤r<1

Moreover, there exists a positive constant γ(λ, p) such that for every f ∈ Lp (∂B(O2 )) the following estimates hold:|c(λ)|kf kp ≤ kPλ f k∗,p ≤ γ(λ, p)kf kp .

(1)

This extends the results in [1] and [2] for classical hyperbolic spaces to the case of the Octonionic Hyperbolic plane
F4(−20) /Spin(9).
To prove the necessary condition, we use the techniques of singular integrals on the boundary ∂B(O2 ) viewed as a space of
homogeneous type in the sense of Coifman and Weiss [5]To prove the sufficiency condition we follow the method we used in [3] and [4], to characterize Poisson integrals of Lp -functions
on the Shilov boundary of bounded symmetric domains.
The talk is based on a joint work with A. Boussejra.
References
1 A. Boussejra, A. Intissar, Caractérisation des intégrales de Poisson-Szegö de L2 (∂Bn ) dans la boule de Bergman B n (n ≥ 2), C. R. Acad. Sci. Paris I(1992), 309-313.
2 A. Boussejra, H. Sami, Characterization of the Lp -range of the Poisson transform in Hyparbolic Spaces B(Fn ), J. Lie. Theory. 12 (2002), 1-14.
3 A. Boussejra, Lp -Poisson integrals representations of solutions of the Hua system on Hermitian symmetric spaces of tube type, J. Funct. Anal. 235(2006), 413-429.
4 A. Boussejra, K. Koufany, Characterization of Poisson integrals for non-tube bounded symmetric domains, J. Math. Pures Appl. 87 (2007), 438-451.
5 R. Coifman, G. Weiss, Extension of Hardy spaces and their use inanalysis, Bull. Amer. Math. Soc. 83 (1977), 569-644.

Aneta Sliżewska (Poland)
Banach-Lie groupoids related to W ∗ -algebra
Abstract. In this presentation we will show that the groupoid of partially invertible elements and in particular the groupoid ofpartial isometries of a W ∗ -algebra have the structure of Banach-Lie groupoids. The relationship between these groupoids andBanach-Poisson geometry will be also disscussed.
References
1 A. Odzijewicz, A. Sliżewska, Banach-Lie groupoids associated to W*-algebras, Symplectic Geom. 14 (2016), no. 3, 687 - 736.
2 A. Odzijewicz, G. Jakimowicz, A. Sliżewska, Banach-Lie algebroids associated to the groupoid of partially invertible elements of a W*-algebra, J.
Geom. Phys. 95 (2015), 108-126.
3 A. Odzijewicz, G. Jakimowicz, A. Sliżewska, Fibre-wise linear Poisson structures related to W*-algebras, J. Geom. Phys. 123 (2018), 385-423.

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Clifford algebras, Clifford analysis and applications
Plenary talks
Paula Cerejeiras (Portugal)
SU (3) symmetries on generalised ternary Clifford algebras
Abstract. In the last decade one observes an increasing interest in the study of more refined structures who model moreaccurately numerous physical problems. While the classic Dirac operator de- scribes structures with SU (2)-symmetries likethe Fermions it is not very useful in other situations. Indeed, quite often problems in optics (polarisation filters) require
analysis of SU (3)-symmetries. Other examples can be found in various scientific fields: the modified Ince equation in laser
optics, the N -body problem, or theoretical descriptions of fundamental interactions based on the quark model. For all ofthese cases, the classic Dirac operator and related function theory do not provide a satisfactory representation. In this talkwe are particularly interested in SU (3)-symmetries. This problem is nowadays mainly modelled by means of supersymmetry.
However, we use another approach, based on ternary generalised Clifford algebras, or Z3 -graded cubic algebras. We provide
a complete algebraic de- scription of such algebras and develop the necessary analytic tools for a consistent function theory.
Uwe Kähler (Portugal)
Clifford-Krein modules with reproducing kernels
Abstract. Classic hypercomplex analysis is intimately linked with elliptic operators, such as the Laplacian or the Dirac operator,
and positive quadratic forms. But there are many applications like the inversion of the crystallographic X-ray transform or or
the study of null-solutions of the ultrahyperbolic Dirac operator which are closely connected with indefinite quadratic forms.
Among other things this is due to the possibility of the underlying Clifford algebra to have a signature (p, q) and, therefore, tobe linked to Pontryagin modules instead of Hilbert modules. Although in the majority of papers Hilbert modules are being
used in this context they are not the right choice as function spaces since they do not reflect the induced geometry. In thistalk we are going to show that Clifford-Krein modules are naturally appearing in this context. We take a particular look
into the case of Clifford-Krein modules with reproducing kernels and use it to study interpolation and sampling problems.

Contributed talks
Dmitry Shirokov (Russia)
Method of averaging in Clifford algebras and applications
Abstract. We consider Reynolds operators of Salingaros group and some other operators in Clifford algebra and present a
relation between these operators and projection operators onto fixed subspaces of Clifford algebras. Using these operators,
we present general solutions of some algebraic systems of equations and systems of field theory equations. Using the methodof averaging in Clifford algebra, we compute the elements that connect two sets of higher-dimensional gamma matrices andgeneralize Hestenes method of computing elements of spin groups to the case of arbitrary dimension.

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Coherent states & wavelets
Plenary talks
Fabio Bagarello (Italy)
Extended kq-representation and bi-coherent states
Abstract. The standard kq-representation can be used to prove that a certain discrete subset of coherent states are completein the Hilbert space of the square-integrable functions. This representation is based on the existence of common generalized
eigenfunctions of the unitary operators
T1 = eiαbq0 ,T2 = eiαbp0 ,(2)
where qb0
= qb0† and pb0= pb†0 .
Here, motivated by the appearance of pseudo-bosonic operators in several quantum systems, we introduce non self-adjoint position and momentum-like operators,
and we use these to construct an extended kq-representation, sharing similar properties with the standard one.
Then we use these properties to analyze the completeness of a set of bi-coherent states.
Peter Balazs (Austria)
Frames and Operators
Abstract. Frame theory is a very rich field in functional analysis, with significant impact in many other branches of mathematics,
but also in theoretical physics and signal processing. For example the theory of continuous frame was developed in the context
of coherent states. While frames have been used extensively for the description of functions, recently they have been used more
and more for analyzing operators. We will focus on two aspects: multipliers and representation of operators.
Operators consisting of a transformation, a point-wise multiplication and a back-transformation play an important role inmany scientific disciplines, like mathematics, signal processing and acoustics. In physics such so called quantization operators
link classical and quantum mechanics. In this context these are so-called frame multipliers.
Those operators correspond to a diagonal operator in the coefficient domain. If we allow full matrices we canrepresent any bounded operator by such a system. Ina dual way, operators can be analyzed by the tensors offrames leading to a discretization scheme, which is for example used for the numerical solution of operator equations (in finite-element or boundary-element methods for example). In this talk we present the basic details offrame theory, talk about their generalizations and special cases (like wavelets). We will give an overview over
the theory of multipliers, the representation of operators, their connections and properties of the tensors of frames.

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ICMMP 2019

In memory of Ahmed Intissar

Hans G. Feichtinger (Austria)
Coherent states, Gabor multipliers, and the Banach Gelfand Triple
Abstract. From the point of view of Abstract Harmonic Analysis (AHA) all we need for Time-Frequency Analyis (TFA) is alocally compact Abelian (LCA) group, which allows us to define the Short-Time or Sliding Window Fourier Transform (STFT)
on the Hilbert space L2 (G). For the case of the Euclidean group G = Rd one can take the Gauss-function as a specific “window”or (thinking of the inversion formula, which allows to rebuild the given function f in L2 (G) from the STFT) the “atom”, i.e.
write it as a (continuous) superposition of time-frequency shifted copies of the atom, the so-called coherent states. Gabor
Analysis goes one step further, by replacing the continuous integral by an infinite sum. Anti-Wick operators (we also callthem STFT-multipliers) are obtained by multiplying the STFT with some function “on phase space” before resynthesis, and in asimilar way Gabor multipliers are obtained by multiplying the Gabor coefficients (indexed by some lattice in phase space) bysome weight factors, before doing synthesis.
The goal of this talk will be to show how results about these operators can be compactly described using the Banach Gelfand
triple (S0 , L2 , S00 ), also known as modulation spaces (M 1 , L2 , M ∞ ). We view the Segal algebra S0 as a Fourier invariant
Banach algebra of test functions, and its dual as a space of “mild” distributions. They can be introduced making use only of
Riemann integrals, without reference to Lebesgue measures and topological vector spaces.
The talk will focus on the usefulness of this perspective for questions in TFA, also indicating how this “rigged Hilbert
space” situation allows to derive robustness properties of e.g. the Gabor frames and Gabor multipliers. Such results are
not possible of one limits the view on the pure Hilbert space setting. Even more importantly one can ask whether the
TFA and Gabor Analysis that can be realized over finite Abelian groups (and which can be implemented in a MATLAB
environment) can be used to reliably approximate their continuous counterpart. Among others we will reveal an approach to the realization of discrete Hermite functions, based on experimental insight. As a matter of fact it coincides
with a method proposed not too long ago by N . Cotfas. It is also the basis for what we consider to be an appropriate implementation of the fractional Fourier transform. The theoretical claims will be illustrated by numerical results.
Jean P. Gazeau (France)
Various generalizations of Glauber-Sudarshan coherent states for Quantum Optics
Abstract. Various generalisations of Glauber-Sudarshan coherent states for quantum optics will be presented in a unified
way, with their statistical properties and their possible role in non-standard quantisations of the classical electromagnetic
field. Some original statistical photon-counting aspects of Perelomov SU(2) and SU(1, 1) coherent states will be emphasized.

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ICMMP 2019

In memory of Ahmed Intissar

Vladimir V. Kisil (UK)
Hidden aspects of coherent states from group representation
Abstract. Coherent states is a widely-used tool in mathematical physics, which exists in several different flavours. The
framework of group representation (aka Gilmore–Perelomov’s coherent states) is a popular one with extensive coverage inmany textbooks. Yet, some its aspects sadly escaped researchers’ attention for a long time. For example, the following simple
observation is very fruitful:
Lemma 0.0.1 (Analyticity of the coherent state transform). [1] Let G be a group and dg be a measure on G. Let ρ be a unitary
representation of G, which can be extended by integration to a vector space V of functions or distributions on G. Let a fiducial vectorφ ∈ H satisfy the equationZd(g) ρ(g)φ dg = 0,

(3)

G

for a fixed distribution d(g) ∈ V . Then, any coherent state transform ṽ(g) = hv, ρ(g)φi obeys the condition:Z¯ R(g) dg ,Dṽ = 0,where D =
d(g)

(4)

G

¯ is the complex conjugation of d(g).
with R being the right regular representation of G and d(g)To illustrate the result we mention a simple corollary: the image spaces of the coherent state transform with n-th Hermite
function consists of harmonic and true n-poly-analytic functions.
Benefits of systematic applications of Lemma 0.0.1 will be demonstrated in the talk by geometrisation of dynamics which canbe obtained from squeezed states and Airy beams. These work was done in collaboration with Fadhel Almalkli [2].

References
1 Vladimir V. Kisil. Erlangen programme at large: an Overview. In S.V. Rogosin and A.A. Koroleva, editors, Advances in Applied Analysis, chapter 1,
pages 1–94. Birkhäuser Verlag, Basel, 2012. arXiv:1106.1686.
2 Fadhel Almalki and Vladimir V. Kisil. Geometric dynamics of a harmonic oscillator, arbitrary minimal uncertainty states and the smallest step 3
nilpotent Lie group. J. Phys. A: Math. Theor, 52:025301, 2019. arXiv:1805.01399.

Contributed talks
Evaldo M. F. Curado (Brazil)
Optimizing Helstrom bound with non-standard coherent states
Abstract.
In quantum information processing, when one tries to distinguish between two non-orthogonalstates through some receiver device, there exists a quantum error probability.
The latter is bounded below by a quantum limit named Helstrom bound.
In this work we study and compare quantum limits
for states which generalize the Glauber-Sudarshan coherent states, like non-linear and (modified) SusskindGlogower coherent states. We show that for the latter ones the Helstrom bound can be significantly lowered.

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ICMMP 2019

In memory of Ahmed Intissar

Francesco Gargano (Italy)
Bi-coherent and Bi-squeezed states in non Hermitian Quantum Mechanics
Abstract. From a mathematical point of view, losing Hermiticity of the Hamiltonian of a physical system implies that theorthonormal basis of its eigenvectors must be replaced by two sets of biorthogonal states, no longer necessarily bases, but
still complete (see [1]). In this context, in recent years, extended versions of the canonical commutation relations have been
considered in details, and the related second-quantized framework produces the so-called pseudo-bosons. In this talk wefirst focus on the the notion of bi-coherent states (BCS) from a strictly mathematically oriented perspective. BCS can beconsidered as a non-hermitian generalization of coherent states, a class of quantum states playing a fundamental role both froma theoretical and an experimental point of view. Moreover, following the construction of the BCS, we generalize a somehow
related class of states, introducing the bi-squeezed states (BSS). They can be considered as a suitable extension of squeezed states,
introduced originally in quantum mechanics in order to describe non-linear processes such as optical parametric oscillations
and four-wave mixing. This generalization of the squeezed states in the context of non-hermitian quantum mechanics arises
from the introduction of suitable squeezing operators, [2]. Existence of BCS and BSS is in general not guaranteed, and theinvestigation on their existence is done for the well known Swanson model.
References
1 Deformed canonical (anti-)commutation relations and non Hermitian Hamiltonians Non-Selfadjoint Operators in Quantum Physics: Mathematical
Aspects (New York: Wiley), Bagarello, Gazeau, Szafraniec Znojil,2015.
2 Bi-squeezed states arising from pseudo-bosons, Bagarello, Gargano, Spagnolo, , J. Phys. A: Math. Theor. 51 455204, 2018

Amel Mazouz (Algeria)
Husimi distribution: correspondence between quantum and classical dynamics
Abstract. The correspondence between classical and quantum mechanics is an important subject for the better inderstanding ofquantum limits.
In particular, it is very important to investigate the correspondence between distribution functions in classical mechanics andin phase space representation of quantum mechanics as well as the Husimi function.
Topics dealt with include formulation of the Husimi representation and it application to analyses coherents and squeezed
states of the 3D harmonic oscillator.

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q-deformation, Hopf algebras and quantum groups
Plenary talks
Abdenacer Makhlouf (France)
q-Deformations and twisted algebraic structures
Abstract. A quantum deformation or q-deformation consists of replacing usual derivation by a σ-derivation or (σ, τ )-derivationin algebras of vector fields. The main example is given by Jackson derivative and lead for example to q-deformation of sl2 , Witt
algebra, Virasoro algebra and also Heisenberg algebras (oscillator algebras). The description of the new structures gave rise to a
structure generalizing Lie algebras, called Hom-Lie algebras or quasi-Lie algebras studied first by Larsson and Silvestrov. Since
then various classical algebraic structures and properties were extended to the Hom-type setting. The main feature is that theclassical identities are twisted by homomorphisms.
The purpose of my talk is to give an overview of recent developments and provide some key constructions and examples on
Hom-algebras and BiHom-algebras. Moreover, I will describe (σ, τ )-differential graded algebra which generalizes the notion ofdifferential graded algebra, and show example involving Clifford algebra.
References
1 V. Abramov, O. Liivapuu and A. Makhlouf, (q, σ, τ )-Differential Graded Algebras. Universe 2018, 4, 138; doi:10.3390/universe4120138 (2018)
2 F. Ammar and A. Makhlouf, Hom-Lie Superalgebras and Hom-Lie admissible Superalgebras, Journal of Algebra, Vol. 324, Issue 7, 1513Ð1528 (2010).
3 G. Graziani, A. Makhlouf, C. Menini, F. Panaite, BiHom-associative algebras, BiHom-Lie algebras and BiHom-bialgebras, Symmetry Integrability
Geom. Methods Appl. 11 (2015), 086, 34 pages.
4 J. T. Hartwig, D. Larsson, S. D. Silvestrov, Deformations of Lie algebras using σ-derivations, J. Algebra 295 (2006), 314–361.
5 A. Makhlouf, S. Silvestrov, Hom-algebras and Hom-coalgebras, J. Algebra Appl. 9 (2010), 553–589.

1938

Geometric mechanics, non-commutative geometry andsymmetry
Plenary talks
Azzouz Awane (Morocco)
Polarized k-symplectic geometry
Abstract.

We study various aspects and properties of polarized k-symplectic manifolds. We give a special interest to
the study of Poisson structures subordinated to polarized k−symplectic structures of differentiable manifolds, and also, we
introduce and study the notion of polarized vectorial Poisson manifold. Some properties and examples are given. The
characteristic foliations of a polarized k-symplectic structure and the almost polarized k−symplectic structures are studied.

Danail Brezov (Bulgaria)
On the Complex Kinematics of Relativity
Abstract. The paper provides an alternative study on the proper Lorentz group SO+ (3, 1) ∼= SO(3, C) in close analogy withthe kinematical treatment of the group of spatial rotations. We first derive the former via projection from the Clifford group of
R3 , which may be considered a complex extension to the set of invertible quaternions H× .
Thus, the Maurer-Cartan form yields a pure bi-quaternion valued analogue of the classical angular velocity de- scribing theaction of SO(3), which serves as a connection form restricted to time-parameterized one-subgroups.
The resulting complex kinematics of SO+ (3, 1) is far richer than the Euclidean one and yet, not too confusing at least in thedecomposable setting, which is our main focus due to its great importance in theoretical physics. In particular, the associatedgeometric phase it yields consists of several distinct counterparts describing well known effects named after Coriolis, Thomas,
Hall and Sagnac. We also consider a restriction to the three real forms, usually referred to in physical literature as ”Wigner little
groups“ and discuss some dynamical aspects.
Finally, we comment on the way imposing different analyticity conditions on the homogeneous (Clifford) co- ordinates affects
the corresponding projective picture and the underlying physics. One major advantage of ourdescription is its clarity and simplicity: each formula it provides comes with a clear geometric interpretation and we are able
to easily pick nice examples from distinct fields such as mechanics, optics and particle physics.
Jerzy Lukierski (Poland)
New Approach to colour symmetries: Dirac equations for quarks and algebraic confinement
Abstract. We propose a modification of standard QCD description of the colour triplet of quarks describing quark fields
endowed with colour degree of freedom by introducing a 12-component colour generalization of Dirac spinor, withbuilt-in
Z3 grading playing an important algebraic role in quark confinement. In colour Dirac equations the SU (3) colour symmetry
is entangled withthe Z3 -graded generalization of Lorentz symmetry, containing three 6-parameter sectors related by Z3
maps. The generalized Lorentz covariance requires simultaneous presence of 12 colour Dirac multiplets, which lead to thedescription of all internal symmetries of quarks: besides SU (3)×SU (2)×U (1),the flavour symmetries and three quark families.
The talk is based on the paper by:
R.Kerner and J.Lukierski, arXiv:1901.10936[hep-th].
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ICMMP 2019

In memory of Ahmed Intissar

Anatol Odzijewicz (Poland)
A family of integrable perturbed Kepler systems
Abstract. It is well known that the 3-dimensional Kepler system could be described, and thus integrated, as a system of four
harmonic oscillators which are tied by a certain quadratic bound, e.g. see [1-4].
We also consider such systems of harmonic oscillators assuming however, that they are interacting in a non-linear way. This
interaction is given by the Hamiltonians
H = H0 (|η1 |2 , |η2 |2 , |ξ1 |2 , |ξ2 |2 )+(5)

G0 (|η1 | , |η2 | , |ξ1 | , |ξ2 | )(η1k η2−k ξ1l ξ2−l + η1−k η2k ξ1−l ξ2l ),
2

2

2

2

where H0 , G0 are arbitrary smooth functions of four real arguments and k, l ∈ Z. Here for z ∈ C and k ∈ Z we assumed theconvention
 kz ,if k ≥ 0
k
z :=
.
(6)
z̄ −k , if k < 0
We will show that such Hamiltonian systems are integrable.
Next, after reduction to the submanifold of null-twistors and applying suitable symplectic diffeomorphisms, we showthat these Hamiltonian systems are equivalent to a 3-dimensional perturbed Kepler systems written in the "fictitious time"
representation, [4,5]. In such a way we obtain a family of 3-dimensional perturbed Kepler systems which are integrated byquadratures, see [5].
The solution of the Hamilton equations for a particular choice of (5) will be explicitly presented.
References
1 T. Iwai, The geometry of the SU (2) Kepler problem, J. Geom. Phys. 7, 507-535, 1990
2 M. Kummer, On the Regularization of the Kepler Problem, Commun. Math. Phys. 84, 133-152, 1982
3 P. Kustaanheimo, E. Stiefel, Perturbation theory of Kepler motion based on spinor regularization, J. Reine Angew. Math. 218, 204-219 (1965)
4 A.Odzijewicz, Perturbed (2n − 1)-dimensional Kepler problem and the nilpotent adjoint orbits of U (n, n), (to appear)
5 A. Odzijewicz, E. Wawreniuk, A. Sliżewska, A family of integrable perturbed Kepler systems, (to appear)

Lassi J.Päivärinta (Estonia)
Scattering of acoustic and electromagnetic waves by screens
Abstract. We study the scattering of electromagnetic (EM) and acoustic waves from thin objects that we call screens, more
precisely , the scatterer is two dimensional object in three dimensional space. The incoming waves are assumed to be timeharmonic. A special difficult and interesting case is when the scatterer has corner points. These impose extra singularities forthe fields.
The goal of this study is to bring new light to the theory of antennas. The basic experiments of antennas were done byHeinrich Herz in 1887. Herz constructed a dipole antenna which proved the existence of electromagnetic waves. We try, instead,to develop a theory for multipole antennas i.e. so called glover model. Some experiments made in Finland indicate that thesemight work better than dipole antenna.
This is a joint study with Sadia Sadique from Tallinn University of Technology.

Contributed talks
Edwin Beggs (Wales)
Geodesics in noncommutative geometry
Abstract. Geodesics play an important part in the theory of general relativity and differential geometry in general.
There is an interpretation of classical geodesics in terms of bimodule connections (with different algebras on each sideof the bimodule). This generalises to noncommutative algebras with calculi. The geodesics are described as pathsin the state space of the algebra, and these states are given by Hilbert C*-modules in quite a simple fashion. The
Hilbert C*-modules also provide a potential link to quantum theory. We shall look at examples from matrices andfunctions on finite groups, as well as first order deformations of classical manifolds. See https://arxiv.org/abs/1811.07601
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ICMMP 2019

In memory of Ahmed Intissar

Briceyda B. Delgado (Russia)
A right inverse operator for curl+λI and applications−−−
Abstract.
In this talk will be presented a general solution of the equation curl →ω + λ→
ω = →g, λ ∈→−
3C, λ 6= 0 for an arbitrary bounded domain Ω ⊂ R with a Liapunov boundary and g in certain classof integrable functions.
The result is given in terms of classical integral operators of quaternionic analy−
sis. Applications of this result are considered to Neumann boundary value problems for the equation curl →
ω +
→
−
→
−
λ ω = g as well as to the nonhomogeneous time-harmonic Maxwell system for achiral and chiral media.
Kamal Diki (Italy)
The slice hyperholomorphic Cholewinski-Fock space on quaternions
Abstract. In this talk, inspired from the Cholewinski approach, we investigate a family of Fock spaces in the quaternionic slice hyperholomorphic setting as well some associated quaternionic linear operators. In a particular case, we reobtain the slice hyperholomorphic Fock space introduced and studied in 2014 by Alpay, Colombo, Sabadini and Salomon.
Alberto Molgado (Mexico)
Polysymplectic structures and general relativistic models
Abstract. A particular interesting issue within the canonical program for the quantisation of relativistic field theories is associated to the absence of a covariant Poisson structure at the classical level. In this direction, we will address a particular version for
the analysis of classical field theories known as the polysymplectic formalism, which allows us to construct a well defined covariant Poisson bracket defined on the set of differential forms associated to the fields and its conjugate polymomenta. Though thisformalism may be equivalent to the Lagrangian formalism at the classical level, the quantum program is far from being complete.
In this talk, we will introduce the basics of the polysymplectic formalism for classical field theories and, at the classical level, we
will explicitly present a couple of models associated to General Relativity. We will discuss certain advantages that the polysymplectic formalism may have in comparison to other approaches. Also, at the quantum level, we will introduce some ideas that we
expect may shed some light on the ingredients that a covariant quantisation of relativistic field theories may need to incorporate.
Zaiem Slimane (Morocco)
Schrödinger Differential equation and Non-commutative geometry
Abstract. We obtain exact solutions of the 2D Schrödinger differential equation for central potentials in non-commutativecomplex space, using the Power-series expansion method. Hence, we can say that the Schrödinger equation in non-commutativecomplex space describes to the particles with spin (1/2) in an external uniform magnitic field. Where the noncommutativity play
the role of magnetic field with created the total magnetic moment of particle with spin 1/2, who in turn shifted the spectrum ofenergy. Such effects are similar to the Zeeman splitting in a ordinare space.

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Orthogonal Polynomials, special functions, exact solvablesystems, non-linear systems
Plenary talks
Mariano A del Olmo (Spain)
Special functions, Lie algebras and rigged Hilbert spaces

Abstract. The aim of this communication is to present a unified picture of the connections between representations of Liealgebras, special functions, discrete and continuous bases and rigged Hilbert spaces.
Each class of orthogonal polynomials is a particular representation of a Lie algebra. This is the case of the Hermite polynomials
and the Heisenberg-Weyl algebra or the associated Laguerre polynomials and the Spherical harmonics with SO(3, 2). Spaces
supporting the representation of these associated algebras include discrete as well as continuous bases of which the matrix
transformation is described by the orthogonal polynomials.
Hilbert spaces are not apt to describe these spaces as they do not have continuous bases. These spaces are quite often used byphysicists, so that it would be necessary to introduce spaces allowing both discrete and continuous bases. They are the rigged
Hilbert spaces.
Nobukazu Shimeno (Japan)
Matrix valued spherical functions on real semisimple Lie groups
Abstract. Let G = KAN be a connected real semisimple Lie group of finite center. We define a notion of “minuscule K-types”,
which is a generalization of the notion of fine K-types for real split Lie groups due to Vogan and the notion of minuscule
K-types for complex Lie groups. Under some additional conditions, there exists a first order invariant differential operatorson the homogeneous vector bundle over G/K associated with a minuscule K-type. Moreover, the matrix valued elementary
spherical functions on G for such a minuscule K-type can be expressed explicitly by Opdam’s non-symmetric hypergeometricfunctions associated with the restricted root system of G/K. We also give some applications in harmonic analyisis for sphericalfunctions.
This talk is based on joint work with Hiroshi Oda.

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ICMMP 2019

In memory of Ahmed Intissar

Hashim A. Yamani (Saudi Arabia)
Supersymmetry of tridiagonal Hamiltonians and their associated orthogonal polynomials
Abstract. We consider a given positive semi-definite Hamiltonian H that has a tridiagonal matrix representation in a basis{|φn i}∞n=0 : Hn,m = hφn |H|φm i = bn−1 δn,m+1 + an δn,m + bn δn,m−1 . Associated with this Hamiltonian is a set of functions {fn (E)}∞n=0 that satisfies the three-term recursion relation: Efn (E) = bn−1 fn−1 (E) + an fn (E) + bn fn (E). If the
Hamiltonian
R {Eµ }µ and a continuous part Ωc (E), then the following orthogonality relation is satisfied
P has a discrete partδn,m = fn (Eµ )fm (Eµ ) + Ωc (E) fn (E)fm (E)dE. The set {pn (E)}∞n=0 , defined by the relation pn (E) associated orthogonalµpolynomials. We then define a forward-shift operator A by its action on the basis: A|φm i = cm |φm i + dm |φm−1 i. The∞∞∞
parameters {cn }∞n=0 and {dn }n=0 can be derived from the sets {an }n=0 and {bn }n=0 , or directly from the polynomials as22cn = −bn [pn+1 (0)/pn (0)] and dn+1 = −bn [pn (0)/pn+1 (0)], where we set the ground state energy equal to zero. This inturn enables us to write the Hamiltonian in the form H = A† A. We then examine the properties of the supersymmetric(+)
partner Hamiltonian H (+) = AA† . We show that it is tridiagonal in the same basis. The associated polynomials {pn (E)}∞
n=0
(+) ∞
(+) ∞
turns out to be the kernel polynomials to {pn (E)}∞.
We
relatethecoefficients
{a
}
and
{b
}
to
the
coefficients
n
n
n=0
n=0
n=0
∞
{an }∞
n=0 and {bn }n=0 .
∞We show that all these coefficients are derivable from the parameters {cn }∞n=0 and {dn }n=0 , which turn out
to be fundamental in this study.
If, further, the Hamiltonian has a shape-invariance property, these parameters completely characterize the spectrum of the Hamiltonian and the hierarchy of its supersymmetric partners.
They also enable us to derive the coherent states associated with the Hamiltonian.
We illustratethese results with examples of known Hamiltonian having tridiagonal matrix representation in known bases.

Contributed talks
Pedro Alberto (Portugal)
Mathematical solutions of Coulomb type tensor interactions in relativistic quantum mechanics
Abstract. The Coulomb potential plays a crucial role in Physics, both in the classical, macro world and in the quantum,
atomic and subatomic world. In this work we find the exact analytical solutions of the equation for a relativistic quantum particle of spin 1/2, i.e., the Dirac equation, for a generalized radial Coulomb potential with a tensor Lorentz structure.
It turns out that the solutions can be expressed in terms of orthogonal polynomials, namely generalized Laguerre polynomials. This fact allows us to determine precisely the node structure of the respective wave functions in terms of thequantum numbers associated with the energy of the bound solutions. At the same time, because of the tensor character of the potential , it favors solutions with a particular alignment of the intrinsic spin and the orbital angular momentum of the quantum particle. We discuss also other special features of some solutions like infinite energy degeneracy.
Abdelhadi Benahmadi (Morocco)
Non-trivial 1d and 2d Segal-Bargmann transforms
We consider the the univariate complex Hermite polynomials and we establish some interesting
Abstract.
summation formulas including special generating functions and Mehler’s formulas. Such results are then employed to introduce and study new integral transforms of Segal-Bargmann between some functional Hilbert spaces.
Zakariyae Mouhcine (Morocco)
An Integral Transform Connecting Spherical Analysis on Harmonic NA Groups to that of Odd Dimensional Real
Hyperbolic Spaces
Abstract. The main aim of the present paper is to establish an integral transform connecting spherical analysis on harmonic
NA groups to that of odd dimensional real hyperbolic spaces. Moreover, certain interesting integral identities for the Gausshypergeometric functions have also been given.

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ICMMP 2019

In memory of Ahmed Intissar

Yahyeh Souleiman (Djibouti)
Numerical Analysis of a Sliding frictional contact problem with Unilateral Contact and Normal Compliance
Abstract. We consider a mathematical model which describes the equilibrium of a viscoelastic body in frictional contact with a moving foundation. The contact is modeled with a multivalued normal compliance condition with unilateral constraint and memory term, associated to a sliding version of Coulomb’s law of dry friction. We present a description of the model, list the assumption on the data and derive a variational formulation of the problem, which isin a form of a system coupling a nonlinear equation for the stress field with a variational inequality for the displacement field. Then, we introduce a fully discrete scheme for the numerical approximation of the sliding contact problem. Under certain solution regularity assumptions, we derive an optimal order error estimate and we provide numerical validation of this result. Finally, we provide some numerical simulations in the study of a two-dimensional problem.
Mohammed Ziyat (Morocco)
Landau level coherent state transforms for quasi-tori
Abstract. The spectrum of the Laplcian operator on theta line bundle over the quasi-torus reduces to eigenvalues π`; ` = 0, 1, · · · ,which are called Landau levels. This paper discusses the coherent state transform for each eigenspace associated with a Landaulevel. We construct an unitary transform valid for some factor of the eigenspace. A concrete form of the inverse formula for the
proposed transform is also obtained.

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Spectral theory and quantum systems, quantum
information
Plenary talks
Pavel Exner (Czech Republic)
On Schrödinger operators exhibiting a parameter-dependent spectral transition
Abstract. In this talk we are going to analyze several classes of Schrödinger operators with potentials that are below unbounded
but their negative part is localized in narrow channels. A prototype of such a behavior can be found in Smilansky-Solomyakmodel devised to illustrate that an an irreversible behavior is possible even if the heat bath to which the systems is coupled
has a finite number of degrees of freedom. We review its properties and analyze several modifications of this model, withregular or strongly singular potentials, or a magnetic field, as well as another system in which xp y p potential is amended by anegative radially symmetric term. All of them have the common property that they exhibit an abrupt parameter-dependent
spectral transition: if the coupling constant exceeds a critical value the spectrum changes from a below bounded, partly or fully
discrete, to the continuous one covering the whole real axis. We also discuss resonance effects in such models. The results comefrom a common work with Diana Barseghyan, Andrii Khrabustovskyi, Jiří Lipovský, Vladimir Lotoreichik, and Miloš Tater.
Jacques Faraut (France)
Horn’s problem from a probabilistic point of view
Abstract. Let A and B be two n × n real symmetric or Hermitian matrices. Assume that the eigenvalues α1 , . . . , αnof A are known, as well as the eigenvalues β1 , . . . , βn of B. What can be said about the eigenvalues of the sum C =A + B ? This is Horn’s problem. The set of symmetric (resp. Hermitian) matrices X with spectrum {α1 , . . . , αn } is anorbit Oα for the natural action of the orthogonal group O(n) on the space of n × n symmetric matrices (resp. of theunitary group U (n) on the space of Hermitian matrices): X 7→ U XU ∗ . Assume that the random matrix X is uniformly
distributed on Oα , and, independently, the random matrix Y is uniformly distributed on Oβ . The problem is now to determine
the joint distribution of the eigenvalues of the sum Z = X + Y . We know a formula for this distribution in case ofHermitian matrices. But in case of symmetric matrices we only know such a formula when the rank of B is equal to one.

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Nelson Faustino (Brazil)
Fractional Fokker-Planck equations on lattices associated to Wilson-Dirac type operators
Abstract. The aim of this talk is centered around the fractional Fokker-Planck equation of the type

1
t2H−1

+
−

 ∂t Ψ(x, t) = (Dh+ Dh)Ψ(x, t) −∆h Ψ(x, t)2
2Γ(2H)Ψ(x, 0) = h1n δ0,x

if

(x, t) ∈ hZn × (0, ∞)if

x ∈ hZn

Hereby Dh± resp. ∆h denote the forward/backward discretization of the Dirac operator D =nX

ej ∂xj resp. Laplace operator

j=1∆ on the lattice hZn (cf. [3]), whereas 0 < H < 1 stands for the Hurst parameter (cf. [1]).
Its content is neatly summarized as follows:• On the first part we will obtain possible conections between the aforementioned evolution problem and the probability
distribution of Mittag-Leffler type Mν (p, t) := p−ν Mν (pt−ν ) (s, t > 0 & 0 < ν < 1), described through the Laplacetransform identities (cf. [6]):
Z ∞

−sp

e
Z0 ∞

Mν (p, t)ds =∞X(−pt−ν )kk=0

e−st Mν (p, t)ds =Γ(νk + 1)νsν−1 e−ps .

0• On the second part we will depict further subordination formulae encoded by the Mittag-Leffler probability distributionMν (p, t) that allows us to reformulate our evolution-type problem in terms of the integro-differential operator ∂tβ +(−∆h )α , carrying the Caputo derivative ∂tβ (0 < β ≤ 1) and the fractional powers of the discrete Laplacian (−∆h )α(0 < α ≤ 1).
Such approach may be seen as a continuation of the approach considered by the author in [4] and goes towards some recent
results obtained by [7] and [2]. It relies on the replacement of the discrete heat type kernel encoded by the semigroup{exp(t∆h )}t≥0 by the Mittag-Leffler distribution Mν (p, t), which allows for applications in settings where the discrete Fouriertransform on the toroidal manifold Rn /hZn may be not the most appropriate tool to represent the symbol of the propagator.
The physical motivations besides are the so-called lattice fermion doubling gap carrying discrete counterparts of continuum
operators (cf. [5]), and Wilson’s regularization approach on the lattice (cf. [8]) endowed by the so-called Wilson-Dirac operatort
1 +(Dh + Dh− ) − ∆h . Indeed, for H → 1− the time variable t may be interpreted as the Wilson parameter so that the solution
2
2

−1
t
1 +
of the aforementioned problem may be seen as a fractional regularization of the propagator(Dh + Dh− ) − ∆h.
22References
1 Bender, C. (2003). An Itô formula for generalized functionals of a fractional Brownian motion with arbitrary Hurst parameter. Stochastic Processes andtheir Applications, 104(1), 81-106.
2 Ciaurri, Ó., Roncal, L., Stinga, P. R., Torrea, J. L., & Varona, J. L. (2018). Nonlocal discrete diffusion equations and the fractional discrete Laplacian,regularity and applications. Advances in Mathematics, 330, 688-738.
3 Faustino, N., Kähler, U., & Sommen, F. (2007). Discrete Dirac operators in Clifford analysis. Advances in Applied Clifford Algebras, 17(3), 451-467.
4 Faustino, N. (2018). Relativistic Wave Equations on the lattice: an operational perspective. arXiv preprint arXiv:1801.09340.
5 Friedan, D. (1982). A proof of the Nielsen-Ninomiya theorem. Communications in Mathematical Physics, 85(4), 481-490.
6 Gorenflo, R., & Mainardi, F. (2012). Parametric subordination in fractional diffusion processes. In Fractional Dynamics: Recent Advances (pp. 229-263).
7 Hahn, M., Kobayashi, K., & Umarov, S. (2011). Fokker-Planck-Kolmogorov equations associated with time-changed fractional Brownian motion.
Proceedings of the American mathematical Society, 139(2), 691-705.
8 Wilson, K. G. (1974). Confinement of quarks. Physical Review D, 10(8), 2445.

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In memory of Ahmed Intissar

Georgi Raikov (Chile)
Resonances and SSF singularities for a magnetic Schroedinger operator
Abstract. I will consider the 3D Schroedinger operator with constant magnetic field, perturbed by a rapidly decaying electric
potential.
First, I will discuss the asymptotic behavior of the corresponding Krein spectral shift function (SSF) near the Landau levels
which play the role of spectral thresholds. I will show that the SSF has singularities near these thresholds, which admit a
fairly explicit description in terms of appropriate Berezin-Toeplitz operators. Further, I will introduce the resonances of theperturbed Schroedinger operator, and will discuss their asymptotic distribution near the spectral thresholds. I will show that
under suitable assumptions on the perturbing potential, there are infinitely many resonances near every fixed Landau level, andthe main asymptotic term of the corresponding resonance counting function is again related to the Berezin-Toeplitz operators
arising in the description of the SSF singularities. Some extensions to Pauli operators with non-constant magnetic fields could
be briefly outlined.
The talk is based on joint works with J.-F. Bony, V. Bruneau, C. Fernández, A. Pushnitski, and S. Warzel.
Tomoyuki Shirai (Japan)
Limit theorems for determinantal point processes
Abstract. The unitary group of size n together with the Haar probability measure is called Circular Unitary Ensemble of sizen. All the eigenvalues lie on the unit circle in the complex plane and they can be regarded as a determinantal point process
on the unit circle. It is also known that the scaled point processes converge to the determinantal point process associatedwith the so-called sine kernel as n tends to ∞. In this talk, we discuss a generalization of this fact and some related topics ondeterminantal point processes.
This talk is based on a joint work with Makoto Katori (Chuo University).
Sébastien Tremblay (Canada)
On generalized powers in one-dimensional supersymmetric quantum mechanics
Abstract. Representation for the general solution of the Sturm-Liouville equation as a spectral parameter power series (SPPS)
was discovered ten years ago [1]. The power series is expressed in terms of a complete systems of recursive integrals generalized
the system of powers (x − x0 )n . These systems of recursive integrals, called generalized powers or ψ0 -powers, are expressedin terms of a nonvanishing function ψ0 representing the ground state when we consider the Schrödinger’s equation. In thelast years, many works of Kravchenko et al. have shown that numerical methods based on SPPS representation is highly
competitive in comparaison to the best available solvers. In this talk we will rather show new results on analytical properties of
the generalized powers for the Schrödinger’s equation and for supersymmetric quantum mechanics.
References
1 Kravchenko, V. V. and Porter, R. M. (2010), Spectral parameter power series for Sturm–Liouville problems. Math. Meth. Appl. Sci., 33: 459-468.
doi:10.1002/mma.1205

Apostol Vourdas (UK)
Fermionic quantum computation and exterior calculus
Abstract. Grassmann’s exterior calculus with its three operations meet, join and hodge star complement, is used for the
representation of fermion-hole systems. The mathematical aspects of exterior calculus are interpreted physically in thiscontext. Two different schemes that implement fermionic quantum computation, are proposed. The first scheme compares
fermionic gates with Boolean gates, and leads to novel electronic devices that simulate fermionic gates. The second scheme
uses a well known map between fermionic and multi-qubit systems, to simulate fermionic gates within multi-qubit systems.

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In memory of Ahmed Intissar

Contributed talks
Abdessamad Belfakir (Morocco)
Generalized Heisenberg algebra: periodicity and finite representation
Abstract. We consider the Generalized Heisenberg Algebra( GHA) and the deformed GHA with finite representations.
We provide the necessary restriction on the characteristic function of the periodic GHA and of the periodic deformed
GHA and study particular examples. Then, we give a deformation of GHA raising operator of the Morse system andconclude that this system can be described by a periodic deformed GHA as it can be deduced from a nilpotente GHA.
Mohammed Berkani (Morocco)
On the B-discrete spectrum
Abstract. In this talk, we introduce the B-discrete spectrum of an unbounded closed operator. Then we prove that a closed
operator has a purely B-discrete spectrum if and only if it has a meromorphic resolvent. An illustrating example of operator
with purely B-discrete spectrum, is given by the Schrödinger operator with a constant magnetic field.
Abdoul Salam Diallo (Senegal)
Affine Szabó manifolds
Abstract. One says that a smooth manifold M of dimension n is a pseudo-Riemannian manifold of signature (p, q) if thetangent bundle T M is equipped with a smooth non-degenerate symmetric inner product g of signature (p, q) where n =p + q. Similarly one says that M is an affine manifold if T M is equipped with a torsion free connection ∇. One saysthat g is Szabó if the eigenvalues of the Szabó operators are constant on the pseudo-sphere bundles of unit timelike andspacelike vectors. We extend this concept from the pseudo-Riemannian to the affine setting to define the notion of an affine
Szabó manifold. We establish some basic results concerning affine Szabó manifolds and exhibit examples of this structure.
Vladimir Jaćimović (Montenegro)
Quasiconformal geometry of a magnetic field
Abstract. We study the system of spin-1/2 particles in a magnetic field with state-dependent Hamiltonian. In this setup,the evolution of of magnetic field is described by a dy- namical system on the group SU (1; 1) of automorphisms of the unit
disc. This approach employs known concepts and results from Complex Analysis and Hyperbolic Geometry to provide amathematical explanation of some quantum effects.
References
1 Vladimir Jaćimović: Magnetization dynamics and geometry: coupled Möbius transformations, Rep. Math. Phys., vol. 81 (3), pp. 347 - 357 (2018).

Igor Kanatchikov (UK)On the spectrum of a hypercomplex quantum operator related to the Yang-Mills mass gap
Abstract. We outline the approach of precanonical quantization fields which leads to a hypercomplex generalization of quantum
mechanics instead of an infinite-dimensional one which follows from the canonical quantization and underlies the standard
quantum field theory. We briefly discuss the relationship between those two approaches to field quantization. By applying
the precanonical quantization to Yang-Mills fields we derive a Clifford-algebra-valued operator whose spectrum is related tothe mass spectrum of quantum excitations of quantum YM field. We present a naive estimation of the distance between thelowest and the first excited state of this operator in the case of quantum SU (2) YM field and call for a further development of
the spectral theory of operators on hypercomplex Hilbert spaces which would allow us to treat the problems emerging fromprecanonical quantization of fields more rigorously.

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Mostafa Mbekhta (Morocco)
Polar decomposition, Aluthge and Mean Transforms
Abstract. In this talk, we give a new proof of the existence and uniqueness of the polar decomposition of a bounded operator
on a Hilbert space. We show that the polar part of T = V |T | the polar decomposition of T , is given by an explicit formula :Z ∞V =T exp(−sT ∗ T )|T |ds.
0
1
1
On the other hand, we are establishing new results on the Aluthge (∆(T ) = |T | 2 V |T | 2 ) and mean (Tb = 12 [V |T | + |T |V ])transforms of a bounded operator acting on a Hilbert space.

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Posters

Souad Abumaryam (Libya)
Identity of Chebyshev Polynomial
Abstract. In this paper, we give some important fact about Chebyshev polynomial and their properties. We investigate someproperties of Chebyshev polynomials arising from their orthogonality, generating function. We derive an interesting identities
for these polynomials such as generating functions, relations between the two kinds of Chebyshev polynomials and integral
representation. Finally, we try to involve an Umbral calculus of Chebyshev polynomial.
References
1 Mason, J. And Handscomb, D. Chebyshev Polynomials. , CRC Press, 2003.
2 Trefethen, N.Approximation Theory and Approximation Practice. , University of Oxford, 2012
3 Roman, S.The Umbral Calculus. , Academic Press, INC. Orlando, Florida, 1984.
4 Rota, G. Kung, J. And Yun, C.Combinatorics The Rota Way. , Cambridge University, 2009.
5 Araci,S. Acikgoz,M. Bagdasaryan,A. And Sen, E. The Legendre polynomials associated with Bernoulli, Euler, Hermite and Bernstein polynomials. ,Turkish Journal for Analysis and Number Theory, 2013. 1

Abdelmoumene Mohamed Adib (Algeria)Light Cone Quantization of Open and Closed String Theories in a canstant NS-B field
Abstract. The main results of a bosonic string theory in presence of a N-S B-Field are the fact that the equations of motion do
not depend on the B-field while the Noether currents can depend on B as the same as the boundary conditions. In particular,
the momentum P depend on the B-field. A great number of works have investigated the covariant quantization of this theory
and shows that the coordinates are non-commutative and that the physical states are subject to the Virasoro conditions,which depend on the B-Field. The B-field dependence of the P momentum makes difficult the definition of the light cone
gauge, in the work of Gianluca Grignani, Marta Orselli and Gordon W. Semenoff. This difficulty is resolved for the closed
bosonic string when it wraps a compactified dimension on which we have the only non-zero component of the B-field. The
periodicity conditions allow then the use of the light cone gauge. In this work, we study the coherence of this model throughthe study of the spectrum and its degeneracy compared to the development of the partition function. New physical states
are possible depending on the P quantum number and the number of wrapping of the closed string on the compactified
direction. In the second step, we have investigated the open string case. The absence of the periodicity condition added tothe boundary conditions, which depend on the B-field, makes the light cone gauge difficult to define. We have proposed one
approach based on the results of the covariant quantization and the use of the light cone coordinates system (in progress)
Mohamed Amazioug (Morocco)
Hierarchy of quantum correlations in atom-optomechanical system
Abstract. In this paper we analyze non-classical correlations between atoms and movable mirror in atom-optomechanicalsystems. This system consisting of an atomic ensemble placed inside an optical nanoresonator with a vibrating mirror. First,
we give the Hamiltonian and the explicit expression of covariance matrix leading to the quantum equations describing the
dynamic evolution of the system. Then, the non-classical correlations are quantified using the logarithmic negativity, andbeyond entanglement we use Gaussian quantum discord. We propose also a scheme for examining the evolution of Gaussianquantum steering and its asymmetry. We show that the entanglement of the two mechanical modes is very strongly related tothe parameters characterizing the environment where the movable mirror evolve, in particular the thermal bath temperature.
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In memory of Ahmed Intissar

Tarik Amtout (Morocco)
Preliminary group classification of the boundary layer equations
Abstract. The preliminary group classification is used for boundary layer equations of a thermo-dependent fluid
around any profile. The equations involve three parameters which are the stress, the conductivity and the pressure gradient. In this work by using optimal system of one-, two-dimensional of sub-algebras, we demonstrate
the existence of constitutive laws that give rise to self-similar solutions compatible with the boundary conditions.
Abdessalem Benammar (Algeria)
Missing data restoration of sinogram in limited-angle computed tomography
Abstract. We present in this work the limited-angle computed tomography, which is an ill-posed inversion problem. This caseoften exists in the industry to allow faster non-destructive testing during production phase. However, the inspection is difficult
to achieve due to the shape and size of the inspected parts. During the last decade, various approaches were proposed for caseof limited-angle. These methods were developed for medical application use and do not take into account physical limitations
specific to industrial materials. The aim of this work is to propose a method, which permits to recover the missing data in
the acquisition of projections using minimizing a function. We tested our method with sinogram obtained from Shepp-Loganphantom containing missing projections. The reconstruction image of inpainted sinogram achived using FBP method and
Iterative cimmino method. The results clearly show that the proposed method can retrieve accurate information that leads to abetter-reconstructed image.
References
1 Yixing Huang, Guenter Lauritsch, Mario Amrehn, Oliver Taubmann, Viktor Haase, Daniel Stromer, Xiaolin Huang, Andreas Maier, “Image Quality
Analysis of Limited Angle Tomography Using the Shift-Variant Data Loss Model”, Bildverarbeitung für die Medizin, pp 277-282, 2016.
2 Hongliang Qi, Zijia Chen, Shuyu Wu, Yuan Xu, Linghong Zhou, “Iterative image reconstruction using modified non-local means filtering for
limited-angle computed tomography”, Physica Medica, Volume 32, Issue 9, pp1041-1051 September 2016.

Amin Benaissa Cherif (Algeria)
Oscillation theorems for higher order neutral nonlinear dynamic equations on time scales
Abstract. we will establish some oscillation criteria for the even-order nonlinear dynamic equation
  n−2 γ ∆2a x∆(t) + f (t, xα (t)) = 0,t ∈ [t0 , +∞)T

(7)

on a time scales T with n is an even integer ≥ 3, where γ and α are the ratios of positive odd integer and a is areal valued
rd-continuous function defined on T.
Iness Haouala (Tunisia)
Polynômes de Jacobi-Dunkl et leur analyse harmonique
RÉSUMÉ
On s’intéresse à l’analyse harmonique associée à l’opérateur de Jacobi-Dunkl sur ] − π/2, π/2[. On rappelle, tout d’abord,
quelques résultats sur les polynômes de Jacobi et on donne une représentation intégrale de Laplace pour les polynômes deJacobi-Dunkl. Ensuite, on présente la transformation de Jacobi-Dunkl ainsi que ses propriétés. Finalement, on introduit
l’opérateur de translation généralisée qui nous servira à définir le nouveau produit de convolution dans ce cadre.
Abstract. We are concerned with the harmonic analysis associated with the Jacobi-Dunkl operator on ] − π/2, π/2[.
We recall, first of all, some results on Jacobi polynomials and we give an integral Laplace representation of
the Jacobi-Dunkl polynomials. Then, we present the Jacobi-Dunkl transform and some of its properties. Finally, we introduce the generalized translation operator, which will be used to define a new convolution product.

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In memory of Ahmed Intissar

Tomas Kalvoda (Czech Republic)
New Family of Symmetric Orthogonal Polynomials and a Solvable Model of a Kinetic Spin Chain
Tomas Kalvoda
Abstract. We study an infinite one-dimensional Ising spin chain where each particle interacts only with its nearest
neighbors and is in contact with a heat bath with temperature decaying hyperbolically along the chain. The time evolution of the magnetization (spin expectation value) is governed by an infinite Jacobi matrix whose spectral problem
leads us to a new two-parameter family of orthogonal polynomials expressible in terms of basic hypergeometric (or qhypergeometric) series. We then study the properties of this family of orthogonal polynomials. Finally, we return to
the Ising model and study the magnetization time evolution. This is joint work with Frantisek Stampach. chain. The
time evolution of the magnetization (spin expectation value) is governed by an infinite Jacobi matrix whose spectral
problem leads us to a new two-parameter family of orthogonal polynomials expressible in terms of basic hypergeometric (or q-hypergeometric) series. We then study the properties of this family of orthogonal polynomials. Finally, we
return to the Ising model and study the magnetization time evolution. This is joint work with Frantisek Stampach.
Fatima Zohra Ladrani (Algeria)
Oscillation theorems for fourth-order nonlinear Dynamic equations on time scales
Abstract. we will establish some oscillation criteria for the fourth-order nonlinear dynamic equation on time scalesp x∆ α ∆ 3 α ∆ 2(t) + f (t, x(τ (t))) = 0(t) + q(t) p x∆

on a time scales, where is α quotient of odd positive integer and > 0.

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(8)

Schedule of talks
Monday, April 1
Time
7:30 - 9:00
9:00 - 10:00
10:00 - 10:30
10:30 - 11:10
11:10 - 11:50
11:50 - 12:30
12:30 - 14:00
14:00 - 14:40
14:40 - 15:20
15:20 - 16:00
16:00 - 16:30

Activity
Registration
Opening
CoffeeG. Hans Feichtinger, Coherent states, Gabor multipliers, and the Banach Gelfand Triple
Pavel Exner, On Schrödinger operators exhibiting a parameter-dependent spectral transition
Omar El-Fallah, Estimates of the singular values of Hankel operators on Bergman spaces
Lunch
Hélène Airault, Matrix operators on symmetric Kaehler domains
Nelson Faustino, Fractional Fokker-Planck equations on lattices associated to Wilson-Diractype operators
Abdenacer Makhlouf, q-Deformations and twisted algebraic structures
Coffee BreakChair

J. P. Gazeau

A. Vourdas

Parallel Sessions
Time
16:30 - 17:00
17:00 - 17:30
17:30 - 18:00

16:30 - 17:00
17:00 - 17:30
17:30 - 18:00

Activity / Room A
Chair
Jasel Berra-Montiel, Towards a representation of Loop Quantum Gravity in the Deformation
Quantization approach
Alberto Molgado, Polysymplectic structures and general relativistic models
A.I. Zayed
Milton dos Santos Ferreira, Gyroharmonic analysis and the continuous wavelet transform on
the ball
Activity / Room B
Fouzia El Wassouli, Wigner transform on line bundle on bounded symmetric spaces
Nadia Ourchane, Characterization of the Lp -range of the Poisson transform on the Octonionic E. Curado
Hyperbolic planeFrancesco Gargano, Bi-coherent and Bi-squeezed states in non Hermitian Quantum Mechanics

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In memory of Ahmed Intissar

Tuesday, April 2
Time
8:30 - 9:10
9:10 - 9:50
9:50 - 10:30
10:30 - 11:00
11:00 - 11:40
11:40 - 12:20
12:20 - 13:00
13:00 - 14:30
14:30 - 15:10
15:10 - 15:50
15:50 - 16:30

Activity
Jacques Faraut, Horn’s problem from a probabilistic point of view
Uwe Kähler, Clifford-Krein modules with reproducing kernels
Danail Brezov, On the Complex Kinematics of Relativity
Coffee BreakAli Baklouti, Harmonic Analysis around monomial representations of exponential solvable
Lie groups
Apostol Vourdas, Fermionic quantum computation and exterior calculus
Azzouz Awane, Polarized k-symplectic geometry
Lunch
Ahmed I. Zayed, Sampling on a disc for a class of linear canonical transforms
Fabio Bagarello, Extended kq-representation and bi-coherent states
Coffee Break

Chair
H. Feichtinger

P. Balazs

S. Berceanu

Parallel Sessions
Time
16:30 - 17:00
17:00 - 17:30
17:30 - 18:00
16:30 - 17:00
17:00 - 17:30
17:30 - 18:00

18:00 - 20:00

Activity / Room A
Achraf Ouald Chaib, The Poisson transform on homogeneous vector bundles overSp(n, 1)/Sp(n) × Sp(1)
Vladimir Jaćimović, Quasiconformal geometry of a magnetic field
Mazouz Amel, Husimi distribution: correspondence between quantum and classical dynamics
Activity / Room B
Kamal Diki, The slice hyperholomorphic Cholewinski-Fock space on quaternions
Youssef Omari, Riesz bases of reproducing kernels in small Fock spaces
Noureddine Imesmad, A characterization of the L2 -range of the Poisson transform on homogeneous line bundles over the matrix ball

Chair

N. Faustino

F. Bagarello

Honoring the memory of Professor Ahmed Intissar

Wednesday, April 3
Time
8:30 - 9:10
9:10 - 9:50

12:20 - 13:00
13:00 - 14:30

Activity
Chair
Mostafa Mbekhta, Polar decomposition, Aluthge and Mean Transforms
Jerzy Lukierski, New Approach to colour symmetries: Dirac equations for quarks and alge- T. Shiraibraic confinement
Nobukazu Shimeno, Matrix valued spherical functions on real semisimple Lie groups
Coffee BreakKhalid Koufany, Conformally covariant bi-differential operators for differential forms
Sébastien Tremblay, On generalized powers in one-dimensional supersymmetric quantum A. Baklouti
mechanics
Evaldo M. F. Curado, Optimizing Helstrom bound with non-standard coherent states
Lunch

14:30

Excursion

9:50 - 10:30
10:30 - 11:00
11:00 - 11:40
11:40 - 12:20

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Thursday, April 4
Time
8:30 - 9:10
9:10 - 9:50
9:50 - 10:30
10:30 - 11:00
11:00 - 11:40

15:10 - 15:50
15:50 - 16:30

Activity
Anatol Odzijewicz, A family of integrable perturbed Kepler systems
Georgi Raikov, Resonances and SSF singularities for a magnetic Schrödinger operator
Vladimir V. Kisil, Hidden aspects of coherent states from group representation
Coffee BreakHashim A. Yamani, Supersymmetry of tridiagonal Hamiltonians and their associatedorthogonal polynomials
Mariano A del Olmo, Special functions, Lie algebras and rigged Hilbert spaces
Peter Balazs, Frames and Operators
Lunch
Stefan Berceanu, Differential geometry on homogeneous spaces attached to the Jacobi
group
Paula Cerejeiras, SU (3) symmetries on generalised ternary Clifford algebras
Coffee Break

19:30

Conference dinner at Chez Ali

11:40 - 12:20
12:20 - 13:00
13:00 - 14:30
14:30 - 15:10

Chair
P. Exner

U. Kähler

L. J. Päivärinta

Friday, April 5
Time
8:30 - 9:10
9:10 - 9:50
9:50 - 10:20
10:20 - 11:00
11:00 - 11:40

Activity
Jean P. Gazeau, Various generalizations of Glauber-Sudarshan coherent states for Quantum
OpticsTomoyuki Shirai, Limit theorems for determinantal point processes
Coffee Break
Lassi J.Päivärinta, Scattering of acoustic and electromagnetic waves by screens
Luís D. Abreu, Planar electrostatics in higher Landau levels

Chair

A. Odzijewicz
M. del Olmo

Parallel Sessions
Time
12:00 - 12:30
12:30 - 13:00
13:00 - 15:00
15:00 - 15:30
15:30 - 16:00
16:00 - 16:30
16:30 - 17:00
17:00 - 17:30
17:30 - 18:00

12:00 - 12:30
12:30 - 13:00
13:00 - 15:00
15:00 - 15:30
15:30 - 16:00
16:00 - 16:30
16:30 - 17:00
17:00 - 17:30
17:30 - 18:00

Activity / Room A
Chair
Dmitry Shirokov, Method of averaging in Clifford algebras and applications
P. Cerejeiras
Briceyda B. Delgado, A right inverse operator for curl+λI and applications
Lunch
Edwin Beggs, Geodesics in noncommutative geometry
Abdelhadi Benahmadi, Non-trivial 1d and 2d Segal-Bargmann transforms
V. V. Kisil
Coffee BreakPedro Alberto, Mathematical solutions of Coulomb type tensor interactions in relativistic
quantum mechanics
Abdessamad Belfakir, Generalized Heisenberg algebra: periodicity and finite representation G. Raikov
Igor Kanatchikov, On the spectrum of a hypercomplex quantum operator related to the
Yang-Mills mass gap
Activity / Room B
Zakariyae Mouhcine, An Integral Transform Connecting Spherical Analysis on Harmonic
NA Groups to that of Odd Dimensional Real Hyperbolic Spaces
Yahyeh Souleiman, Numerical Analysis of a Sliding frictional contact problem with Unilateral S. Tremblay
Contact and Normal Compliance
Lunch
Mohammed Berkani, On the B-discrete spectrum
D. Brezov
Aneta Sliżewska, Banach-Lie groupoids related to W ∗ -algebra
Coffee Break
Abdoul Salam Diallo, Affine Szabó manifolds
Zaiem Slimane, Schrödinger Differential equation and Non-commutative geometry
L. D. Abreu
Mohammed Ziyat, Landau level coherent state transforms for quasi-tori
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Acknowledgments

The organisers of the ICMMP - International Conference on Mathematical Methods in Physics wish to thank the many Moroccan
companies who’s financial support was crucial for the success of this event:• SCR - Société Centrale de Réassurance• CARC - The African Centre for Catastrophe Risks• CAT - Company d’Assurance Transport• AXELI - Services Informatique et infogérance• ANRT - Agence Nationale de Réglementation des Télécommunications• GASUP - Le Groupement d’Assurances du Supérieur• SARL - Work Bureau-Béni Mellal
Our sincere gratitude goes also to the Research Center CIDMA, University of Aveiro in Portugal, to Sultan Moulay Slimane
University, and to the Ibn Tofail University for their financial support. Furthermore, our deepest thanks goes to the Faculty of
Sciences and Technics of Béni Mellal which has provided us with both financial and logistical support.
Last but certainly not least, the conference would not have been possible without the great support of the Riyad Mogador
Kasbah Hotel which, by their logistical and administrative support, and the continuous help of its staff members, greatly
facilitated the travel and stay of the participants.

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ICMMP 2019

In memory of Ahmed Intissar

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