pinecone/core-2020-05-10-deduplication huggingface dataset:
Localized boundary-domain singular integral equations based on harmonic parametrix for divergence-form elliptic PDEs with variable matrix coefficients

This is the post-print version of the Article. The official publised version can be accessed from the links below. Copyright @ 2013 Springer BaselEmploying the localized integral potentials associated with the Laplace operator, the Dirichlet, Neumann and Robin boundary value problems for general variable-coefficient divergence-form second-order elliptic partial differential equations are reduced to some systems of localized boundary-domain singular integral equations. Equivalence of the integral equations systems to the original boundary value problems is proved. It is established that the corresponding localized boundary-domain integral operators belong to the Boutet de Monvel algebra of pseudo-differential operators. Applying the Vishik-Eskin theory based on the factorization method, the Fredholm properties and invertibility of the operators are proved in appropriate Sobolev spaces.This research was supported by the grant EP/H020497/1: "Mathematical Analysis of Localized Boundary-Domain Integral Equations for Variable-Coefficient Boundary Value Problems" from the EPSRC, UK
Variation of discrete spectra for non-selfadjoint perturbations of
  selfadjoint operators

Let B=A+K where A is a bounded selfadjoint operator and K is an element of
the von Neumann-Schatten ideal S_p with p>1. Let {\lambda_n} denote an
enumeration of the discrete spectrum of B. We show that $\sum_n
\dist(\lambda_n, \sigma(A))^p$ is bounded from above by a constant multiple of
|K|_p^p. We also derive a unitary analog of this estimate and apply it to
obtain new estimates on zero-sets of Cauchy transforms.Comment: Differences to previous version: Extended Introduction, new Section
  5, additional references. To appear in Int. Eq. Op. Theor
Normal projections in Krein spaces

Given a complex Krein space  H  with fundamental symmetry J, the aim of this note is to characterize the set of J-normal projections
Q={Q∈L(H):Q2=QandQ#Q=QQ#}.
The ranges of the projections in  QQ  are exactly those subspaces of  HH  which are pseudo-regular. For a fixed pseudo-regular subspace  S , there are infinitely many J-normal projections onto it, unless  SS  is regular. Therefore, most of the material herein is devoted to parametrizing the set of J-normal projections onto a fixed pseudo-regular subspace  S.Fil: Maestripieri, Alejandra Laura. Universidad de Buenos Aires. Facultad de Ingeniería; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática; ArgentinaFil: Martinez Peria, Francisco Dardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas; Argentin
Spectral estimates for resolvent differences of self-adjoint elliptic operators

The concept of quasi boundary triples and Weyl functions from extension theory of symmetric operators in Hilbert spaces is developed further and spectral estimates for resolvent differences of two self-adjoint extensions in terms of general operator ideals are proved. The abstract results are applied to self-adjoint realizations of second order elliptic differential operators on bounded and exterior domains, and partial differential operators with δ-potentials supported on hypersurfaces are studied
The Riesz basis property of an indefinite Sturm-Liouville problem with
  non-separated boundary conditions

We consider a regular indefinite Sturm-Liouville eigenvalue problem \{$-f" +
q f = \lambda r f$} on $[a,b]$ subject to general self-adjoint boundary
conditions and with a weight function $r$ which changes its sign at finitely
many, so-called turning points. We give sufficient and in some cases necessary
and sufficient conditions for the Riesz basis property of this eigenvalue
problem. In the case of separated boundary conditions we extend the class of
weight functions $r$ for which the Riesz basis property can be completely
characterized in terms of the local behavior of $r$ in a neighborhood of the
turning points. We identify a class of non-separated boundary conditions for
which, in addition to the local behavior of $r$ in a neighborhood of the
turning points, local conditions on $r$ near the boundary are needed for the
Riesz basis property. As an application, it is shown that the Riesz basis
property for the periodic boundary conditions is closely related to a regular
HELP-type inequality without boundary conditions.Comment: Integr. Equat. Oper. Theory (2013), to appea
A unifying approach to Weyl type theorems for Banach space operators

Weyl type theorems have been proved for a considerably large number of classes of operators. In this paper, by introducing the class of quasi totally hereditarily normaloid operators, we obtain a theoretical and general framework from which Weyl type theorems may be promptly established for many of these classes of operators.  This framework also entails Weyl type theorems for perturbations f(T+K), where  K is algebraic and commutes with T, and f is an analytic function, defined on an open neighborhood of the spectrum of $T+K, such that f is non constant on each of the components of its domain
Carleson Measures, Riemann-Stieltjes and Multiplication Operators on a General Family of Function Spaces

Let $\mu$ be a nonnegative Borel measure on the unit disk of the complex plane. We characterize those measures $\mu$ such that the general family of spaces of analytic functions, $F (p,q,s)$ which contain many classical function spaces, including the Bloch space, $BMOA$ and the $Q_s$ spaces, are embedded boundedly or compactly into the tent-type spaces $T_{p,s}^\infty(\mu)$. The results are applied to characterize boundedness and compactness of Riemann-Stieltjes operators and multiplication operators on $F (p,q,s)$
On positivity and roots in operator algebras

In earlier papers the second author and Charles Read have introduced and
studied a new notion of positivity for operator algebras, with an eye to
extending certain C*-algebraic results and theories to more general algebras.
The present paper consists of complements to some facts in the just mentioned
papers, concerning this notion of positivity. For example we prove a result on
the numerical range of products of the roots of commuting operators with
numerical range in a sector.Comment: 11 pages, to appear Integral Equations Operator Theor
Riemann–Hilbert problems, Toeplitz operators and Q-classes

We generalize the notion of Q-classes C(Q1,Q2) , which was introduced in the context of Wiener–Hopf factorization, by considering very general 2 × 2 matrix functions Q1, Q2. This allows us to use a
mainly algebraic approach to obtain several equivalent representations for each class, to study the intersections of Q-classes and to explore their close connection with certain non-linear scalar equations. The results are applied to various factorization problems and to the study of Toeplitz operators with symbol in a Q-class. We conclude with a group theoretic interpretation of some of the main results.Fundação para a Ciência e a Tecnologia (FCT/Portugal), through Project PTDC/MAT/121837/2010 and Project Est- C/MAT/UI0013/2011. The first author was also supported by the Center for Mathematical
Analysis, Geometry, and Dynamical Systems and the second author was also supported by the Centre of Mathematics of the University of Minho through the FEDER Funds Programa Operacional Factores de Competitividade COMPET
Around the Van Daele–Schmüdgen Theorem

For a {bounded} non-negative self-adjoint operator acting in a complex, infinite-dimensional, separable Hilbert space H and possessing a dense range R we propose a new approach to characterisation of phenomenon concerning the existence of subspaces M\subset H such that M\capR=M^\perp\capR=\{0\}. We show how the existence of such subspaces leads to various {pathological} properties of {unbounded} self-adjoint operators related to von Neumann theorems \cite{Neumann}--\cite{Neumann2}. We revise the von Neumann-Van Daele-Schm\"udgen assertions \cite{Neumann}, \cite{Daele}, \cite{schmud} to refine them. We also develop {a new systematic approach, which allows to construct for any {unbounded} densely defined symmetric/self-adjoint operator T infinitely many pairs of its closed densely defined restrictions T_k\subset T such that \dom(T^* T_{k})=\{0\} (\Rightarrow \dom T_{k}^2=\{0\}$) k=1,2 and \dom T_1\cap\dom T_2=\{0\}, \dom T_1\dot+\dom T_2=\dom T
Non-negative spectral measures and representations of C*-algebras

Regular normalized W-valued spectral measures on a compact Hausdorff space X
are in one-to-one correspondence with unital *-representations \rho:C(X)\to W,
where W stands for a von Neumann algebra. In this paper we show that for every
compact Hausdorff space X and every von Neumann algebras W_1,W_2 there is a
one-to-one correspondence between unital *-representations \rho:C(X,W_1)\to W_2
and special B(W_1,W_2)-valued measures on X that we call non-negative spectral
measures. Such measures are special cases of non-negative measures that we
introduced in our previous paper in connection with moment problems for
operator polynomials.Comment: 20 page
Crossed products for interactions and graph algebras

We consider Exel's interaction $(V,H)$ over a unital $C^*$-algebra $A$, such
that $V(A)$ and $H(A)$ are hereditary subalgebras of $A$. For the associated
crossed product, we obtain a uniqueness theorem, ideal lattice description,
simplicity criterion and a version of Pimsner-Voiculescu exact sequence. These
results cover the case of crossed products by endomorphisms with hereditary
ranges and complementary kernels. As model examples of interactions not coming
from endomorphisms we introduce and study in detail interactions arising from
finite graphs.
  The interaction $(V,H)$ associated to a graph $E$ acts on the core $F_E$ of
the graph algebra $C^*(E)$. By describing a partial homeomorphism of
$\widehat{F}_E$ dual to $(V,H)$ we find Cuntz-Krieger uniqueness theorem,
criteria for gauge-invariance of all ideals and simplicity of $C^*(E)$ as
results concerning reversible noncommutative dynamics. We also provide a new
approach to calculation of $K$-theory of $C^*(E)$ using only an induced partial
automorphism of $K_0(F_E)$ and the six-term exact sequence.Comment: The term complete interaction changed to corner interaction. This
  version is accepted to Integral Equations and Operator Theor
Remarks on the convergence of pseudospectra

We establish the convergence of pseudospectra in Hausdorff distance for
closed operators acting in different Hilbert spaces and converging in the
generalised norm resolvent sense. As an assumption, we exclude the case that
the limiting operator has constant resolvent norm on an open set. We extend the
class of operators for which it is known that the latter cannot happen by
showing that if the resolvent norm is constant on an open set, then this
constant is the global minimum. We present a number of examples exhibiting
various resolvent norm behaviours and illustrating the applicability of this
characterisation compared to known results.Comment: 16 pages, 1 figur
Dobrushin's ergodicity coefficient for Markov operators on cones

We give a characterization of the contraction ratio of bounded linear maps in
Banach space with respect to Hopf's oscillation seminorm, which is the
infinitesimal distance associated to Hilbert's projective metric, in terms of
the extreme points of a certain abstract "simplex". The formula is then applied
to abstract Markov operators defined on arbitrary cones, which extend the row
stochastic matrices acting on the standard positive cone and the completely
positive unital maps acting on the cone of positive semidefinite matrices. When
applying our characterization to a stochastic matrix, we recover the formula of
Dobrushin's ergodicity coefficient. When applying our result to a completely
positive unital map, we therefore obtain a noncommutative version of
Dobrushin's ergodicity coefficient, which gives the contraction ratio of the
map (representing a quantum channel or a "noncommutative Markov chain") with
respect to the diameter of the spectrum. The contraction ratio of the dual
operator (Kraus map) with respect to the total variation distance will be shown
to be given by the same coefficient. We derive from the noncommutative
Dobrushin's ergodicity coefficient an algebraic characterization of the
convergence of a noncommutative consensus system or equivalently the ergodicity
of a noncommutative Markov chain.Comment: An announcement of some of the present results has appeared in the
  Proceedings of the ECC 2013 conference (Zurich). Further results can be found
  in the companion arXiv:1302.522
A family of domains associated with $\mu$-synthesis

We introduce a family of domains --- which we call the $\mu_{1,n}$-quotients
--- associated with an aspect of $\mu$-synthesis. We show that the natural
association that the symmetrized polydisc has with the corresponding spectral
unit ball is also exhibited by the $\mu_{1,n}$-quotient and its associated unit
"$\mu_E$-ball". Here, $\mu_E$ is the structured singular value for the case $E
= \{[w]\oplus(z I_{n-1})\in \mathbb{C}^{n\times n}: z,w\in \mathbb{C}\}$, n =
2, 3, 4,... Specifically: we show that, for such an $E$, the Nevanlinna-Pick
interpolation problem with matricial data in a unit "$\mu_E$-ball", and in
general position in a precise sense, is equivalent to a Nevanlinna-Pick
interpolation problem for the associated $\mu_{1,n}$-quotient. Along the way,
we present some characterizations for the $\mu_{1,n}$-quotients.Comment: 15 pages; added Remark 3.6 and an additional reference; to appear in
  Integral Eqns. Operator Theor
k-Extreme Points in Symmetric Spaces of Measurable Operators

Let $\mathcal{M}$ be a semifinite von Neumann algebra with a faithful,
normal, semifinite trace $\tau$ and $E$ be a strongly symmetric Banach function
space on $[0,\tau(1))$. We show that an operator $x$ in the unit sphere of
$E\left(\mathcal{M},\tau\right)$ is $k$-extreme, $k\in\mathbb N$, whenever its
singular value function $\mu(x)$ is $k$-extreme and one of the following
conditions hold (i) $\mu(\infty,x)=\lim_{t\to\infty}\mu(t,x)=0$ or (ii)
$n(x)\mathcal{M} n(x^*)=0$ and $|x|\geq \mu(\infty,x)s(x)$, where $n(x)$ and
$s(x)$ are null and support projections of $x$, respectively. The converse is
true whenever $\mathcal{M}$ is non-atomic. The global $k$-rotundity property
follows, that is if $\mathcal{M}$ is non-atomic then $E$ is $k$-rotund if and
only if $E\left(\mathcal{M},\tau\right)$ is $k$-rotund. As a consequence of the
noncommutive results we obtain that $f$ is a $k$-extreme point of the unit ball
of the strongly symmetric function space $E$ if and only if its decreasing
rearrangement $\mu(f)$ is $k$-extreme and $|f|\geq \mu(\infty,f)$. We conclude
with the corollary on orbits $\Omega(g)$ and $\Omega'(g)$. We get that $f$ is a
$k$-extreme point of the orbit $\Omega(g)$, $g\in L_1+L_{\infty}$, or
$\Omega'(g)$, $g\in L_1[0,\alpha)$, $\alpha<\infty$, if and only if
$\mu(f)=\mu(g)$ and $|f|\geq \mu(\infty,f)$. From this we obtain a
characterization of $k$-extreme points in Marcinkiewicz spaces.Comment: The final publication is available at Springer via
  http://dx.doi.org/10.1007/s00020-014-2206-
Coefficient multipliers of growth spaces of harmonic functions

Let $h_g^\infty$ be the space of harmonic functions in the unit ball that are
bounded by some increasing radial function $g(r)$ with $\lim_{r\rightarrow 1}
g(r)=+\infty$; these spaces are called growth spaces. We describe functions in
growth spaces by the Ces\`aro means of their expansions in harmonic polynomials
and apply this characterization to study coefficient multipliers between growth
spaces. A series of examples of multipliers is given and some results by A. L.
Shields and D. L. Williams and G. Bennett, D. A. Stegenga and R. M. Timoney are
generalized to harmonic functions in higher dimensions.Comment: Theorem 3 is added, small corrections are mad
Integral Equations for Electromagnetic Scattering at Multi-Screens

International audienceIn [X. Claeys and R. Hiptmair, Integral equations on multi-screens. Integral Equ Oper Theory, 77(2):167–197, 2013] we developed a framework for the analysis of boundary integral equations for acoustic scattering at so-called multi-screens, which are arbitrary arrangements of thin panels made of impenetrable material. In this article we extend these considerations to boundary integral equations for electromagnetic scattering. We view tangential multi-traces of vector fields from the perspective of quotient spaces and introduce the notion of single-traces and spaces of jumps. We also derive representation formulas and establish key properties of the involved potentials and related boundary operators. Their coercivity will be proved using a splitting of jump fields. Another new aspect emerges in the form of surface differential operators linking various trace spaces
The Multidimensional Moment Problem with Complexity Constraint

A long series of previous papers have been devoted to the (one-dimensional)
moment problem with nonnegative rational measure. The rationality assumption is
a complexity constraint motivated by applications where a parameterization of
the solution set in terms of a bounded finite number of parameters is required.
In this paper we provide a complete solution of the multidimensional moment
problem with a complexity constraint also allowing for solutions that require a
singular measure added to the rational, absolutely continuous one. Such
solutions occur on the boundary of a certain convex cone of solutions. In this
paper we provide complete parameterizations of all such solutions. We also
provide errata for a previous paper in this journal coauthored by one of the
authors of the present paper.Comment: 25 pages. Revision: minor correction
The state space isomorphism theorem for discrete-time infinite-dimensional systems

It is well-known that the state space isomorphism theorem fails in infinite-dimensional Hilbert spaces: there exist minimal discrete-time systems (with Hilbert space state spaces) which have the same impulse response, but which are not isomorphic. We consider discrete-time systems on locally convex topological vector spaces which are Hausdorff and barrelled and show that in this setting the state space isomorphism theorem does hold. In contrast to earlier work on topological vector spaces, we consider a definition of minimality based on dilations and show how this necessitates certain definitions of controllability and observability
New relations between discrete and continuous transition operators on
  (metric) graphs

We establish several new relations between the discrete transition operator,
the continuous Laplacian and the averaging operator associated with
combinatorial and metric graphs. It is shown that these operators can be
expressed through each other using explicit expressions. In particular, we show
that the averaging operator is closely related with the solutions of the
associated wave equation. The machinery used allows one to study a class of
infinite graphs without assumption on the local finiteness.Comment: 32 page
A hypocoercivity related ergodicity method with rate of convergence for
  singularly distorted degenerate Kolmogorov equations and applications

In this article we develop a new abstract strategy for proving ergodicity
with explicit computable rate of convergence for diffusions associated with a
degenerate Kolmogorov operator L. A crucial point is that the evolution
operator L may have singular and nonsmooth coefficients. This allows the
application of the method e.g. to degenerate and singular particle systems
arising in Mathematical Physics. As far as we know in such singular cases the
relaxation to equilibrium can't be discussed with the help of existing
approaches using hypoellipticity, hypocoercivity or stochastic Lyapunov type
techniques. The method is formulated in an L2-Hilbert space setting and is
based on an interplay between Functional Analysis and Stochastics. Moreover, it
implies an ergodicity rate which can be related to L2-exponential convergence
of the semigroup. Furthermore, the ergodicity method shows up an interesting
analogy with existing hypocoercivity approaches. In the first application we
discuss ergodicity of the N-particle degenerate Langevin dynamics with singular
potentials. The dual to this equation is also called the kinetic Fokker-Planck
equation with an external confining potential. In the second example we apply
the method to the so-called (degenerate) spherical velocity Langevin equation
which is also known as the fiber lay-down process arising in industrial
mathematics.Comment: Older preprint version of the paper (from 2014). The final
  publication is available at Springer via
  http://dx.doi.org/10.1007/s00020-015-2254-1 It was published under the name
  "A hypocoercivity related ergodicity method for singularly distorted
  non-symmetric diffusions"; see Integral Equations Oper. Theory 83, No. 3,
  Article ID 2254, 331-379 (2015
Berger measure for some transformations of subnormal weighted shifts

A subnormal weighted shift may be transformed to another shift in various
ways, such as taking the p-th power of each weight or forming the Aluthge
transform. \ We determine in a number of cases whether the resulting shift is
subnormal, and, if it is, find a concrete representation of the associated
Berger measure, directly for finitely atomic measures, and using both Laplace
transform and Fourier transform methods for more complicated measures. \
Alternatively, the problem may be viewed in purely measure-theoretic terms as
the attempt to solve moment matching equations such as $(\int t^n \, d\mu(t))^2
= \int t^n \, d\nu(t)$ ($n=0, 1, \ldots$) for one measure given the other
Cartan subalgebras in C*-algebras of Hausdorff etale groupoids

The reduced $C^*$-algebra of the interior of the isotropy in any Hausdorff
\'etale groupoid $G$ embeds as a $C^*$-subalgebra $M$ of the reduced
$C^*$-algebra of $G$. We prove that the set of pure states of $M$ with unique
extension is dense, and deduce that any representation of the reduced
$C^*$-algebra of $G$ that is injective on $M$ is faithful. We prove that there
is a conditional expectation from the reduced $C^*$-algebra of $G$ onto $M$ if
and only if the interior of the isotropy in $G$ is closed. Using this, we prove
that when the interior of the isotropy is abelian and closed, $M$ is a Cartan
subalgebra. We prove that for a large class of groupoids $G$ with abelian
isotropy---including all Deaconu--Renault groupoids associated to discrete
abelian groups---$M$ is a maximal abelian subalgebra. In the specific case of
$k$-graph groupoids, we deduce that $M$ is always maximal abelian, but show by
example that it is not always Cartan.Comment: 14 pages. v2: Theorem 3.1 in v1 incorrect (thanks to A. Kumjain for
  pointing out the error); v2 shows there is a conditional expectation onto $M$
  iff the interior of the isotropy is closed. v3: Material (including some
  theorem statements) rearranged and shortened. Lemma~3.5 of v2 removed. This
  version published in Integral Equations and Operator Theor
On invariant graph subspaces

In this paper we discuss the problem of decomposition for unbounded $2\times
2$ operator matrices by a pair of complementary invariant graph subspaces.
Under mild additional assumptions, we show that such a pair of subspaces
decomposes the operator matrix if and only if its domain is invariant for the
angular operators associated with the graphs. As a byproduct of our
considerations, we suggest a new block diagonalization procedure that resolves
related domain issues. In the case when only a single invariant graph subspace
is available, we obtain block triangular representations for the operator
matrices.Comment: 21 pages. This paper provides a complete overhaul and extension to
  the authors previous work arXiv:1307.6439 and includes an exampl