pinecone/core-2020-05-10-deduplication huggingface dataset:
Bari-Markus property for Riesz projections of 1D periodic Dirac operators

The Dirac operators\ud
\ud
Ly = i ((1)(0) (0)(-1))dy/dx + v(x)y, y = ((y1)(y2)), x is an element of[0, pi],\ud
\ud
with L-2-potentials\ud
\ud
v(x) = ((0)(Q(x)) (P(x))(0)), P, Q is an element of L-2([0, pi]), considered on [0, pi] with periodic, antiperiodic or Dinchlet boundary conditions (bc), have discrete spectra, and the Riesz projections,\ud
\ud
S-N = 1/2 pi iota integral(vertical bar z vertical bar=N - 1/2) (z - L-bc)(-1) dz. p(n) = 1/2 pi iota integral(vertical bar z-n vertical bar=1/2) (z - L-bc)(-1) dz\ud
\ud
are well-defined for vertical bar n vertical bar >= N if N is sufficiently large. It is proved that\ud
\ud
Sigma(vertical bar n vertical bar>N) parallel to P-n - P-n(0)parallel to(2) < infinity, where P-n(0), n is an element of Z,\ud
\ud
are the Riesz projections of the free operator.\ud
\ud
Then, by the Ban Markus criterion, the spectral Riesz decompositions\ud
\ud
f = SN + Sigma(vertical bar n vertical bar>N) P(n)f, for all f is an element of L-2\ud
\ud
converge unconditionally in L-2. (C) 2010 WILEY-VCH Verlag GmbH & Co KGaA, Weinho
The Krein-von Neumann Extension and its Connection to an Abstract
  Buckling Problem

We prove the unitary equivalence of the inverse of the Krein--von Neumann
extension (on the orthogonal complement of its kernel) of a densely defined,
closed, strictly positive operator, $S\geq \epsilon I_{\mathcal{H}}$ for some
$\epsilon >0$ in a Hilbert space $\mathcal{H}$ to an abstract buckling problem
operator.
  In the concrete case where $S=\bar{-\Delta|_{C_0^\infty(\Omega)}}$ in
$L^2(\Omega; d^n x)$ for $\Omega\subset\mathbb{R}^n$ an open, bounded (and
sufficiently regular) domain, this recovers, as a particular case of a general
result due to G. Grubb, that the eigenvalue problem for the Krein Laplacian
$S_K$ (i.e., the Krein--von Neumann extension of $S$), \[ S_K v = \lambda v,
\quad \lambda \neq 0, \] is in one-to-one correspondence with the problem of
{\em the buckling of a clamped plate}, \[ (-\Delta)^2u=\lambda (-\Delta) u
\text{in} \Omega, \quad \lambda \neq 0, \quad u\in H_0^2(\Omega), \] where $u$
and $v$ are related via the pair of formulas \[ u = S_F^{-1} (-\Delta) v, \quad
v = \lambda^{-1}(-\Delta) u, \] with $S_F$ the Friedrichs extension of $S$.
  This establishes the Krein extension as a natural object in elasticity theory
(in analogy to the Friedrichs extension, which found natural applications in
quantum mechanics, elasticity, etc.).Comment: 16 page
Complex valued Ray--Singer torsion II

In this paper we extend Witten-Helffer-Sj\"ostrand theory from selfadjoint
Laplacians based on fiber wise Hermitian structures, to non-selfadjoint
Laplacians based on fiber wise non-degenerate symmetric bilinear forms. As an
application we verify, up to sign, the conjecture about the comparison of the
Milnor-Turaev torsion with the complex valued analytic torsion, for odd
dimensional manifolds. This is done along the lines of Burghelea, Friedlander
and Kappeler's proof of the Cheeger-M\"uller theorem.Comment: 35 page
Changes of variables in modulation and Wiener amalgam spaces

In this paper various properties of global and local changes of variables as well as properties of canonical transforms are investigated on modulation and Wiener amalgam spaces. We establish several relations among localisations of such spaces and, as a consequence, we obtain several versions of local and global Beurling–Helson type theorems. We also establish a number of positive results such as local boundedness of canonical transforms on modulation spaces, properties of homogeneous changes of variables, and local continuity of Fourier integral operators on equation image. Finally, counterparts of these results are discussed for spaces on the torus
On the X-rank with respect to linear projections of projective varieties

In this paper we improve the known bound for the $X$-rank $R_{X}(P)$ of an
element $P\in {\mathbb{P}}^N$ in the case in which $X\subset {\mathbb P}^n$ is
a projective variety obtained as a linear projection from a general
$v$-dimensional subspace $V\subset {\mathbb P}^{n+v}$. Then, if $X\subset
{\mathbb P}^n$ is a curve obtained from a projection of a rational normal curve
$C\subset {\mathbb P}^{n+1}$ from a point $O\subset {\mathbb P}^{n+1}$, we are
able to describe the precise value of the $X$-rank for those points $P\in
{\mathbb P}^n$ such that $R_{X}(P)\leq R_{C}(O)-1$ and to improve the general
result. Moreover we give a stratification, via the $X$-rank, of the osculating
spaces to projective cuspidal projective curves $X$. Finally we give a
description and a new bound of the $X$-rank of subspaces both in the general
case and with respect to integral non-degenerate projective curves.Comment: 10 page
Fine compactified Jacobians

We study Esteves's fine compactified Jacobians for nodal curves. We give a
proof of the fact that, for a one-parameter regular local smoothing of a nodal
curve $X$, the relative smooth locus of a relative fine compactified Jacobian
is isomorphic to the N\'eron model of the Jacobian of the general fiber, and
thus it provides a modular compactification of it. We show that each fine
compactified Jacobian of $X$ admits a stratification in terms of certain fine
compactified Jacobians of partial normalizations of $X$ and, moreover, that it
can be realized as a quotient of the smooth locus of a suitable fine
compactified Jacobian of the total blowup of $X$. Finally, we determine when a
fine compactified Jacobian is isomorphic to the corresponding Oda-Seshadri's
coarse compactified Jacobian.Comment: 35 pages; final version, to appear in Math. Nac
Singularities of slice regular functions

Beginning in 2006, G. Gentili and D.C. Struppa developed a theory of regular
quaternionic functions with properties that recall classical results in complex
analysis. For instance, in each Euclidean ball centered at 0 the set of regular
functions coincides with that of quaternionic power series converging in the
same ball. In 2009 the author proposed a classification of singularities of
regular functions as removable, essential or as poles and studied poles by
constructing the ring of quotients. In that article, not only the statements,
but also the proving techniques were confined to the special case of balls
centered at 0. In a subsequent paper, F. Colombo, G. Gentili, I. Sabadini and
D.C. Struppa (2009) identified a larger class of domains, on which the theory
of regular functions is natural and not limited to quaternionic power series.
The present article studies singularities in this new context, beginning with
the construction of the ring of quotients and of Laurent-type expansions at
points other than the origin. These expansions, which differ significantly from
their complex analogs, allow a classification of singularities that is
consistent with the one given in 2009. Poles are studied, as well as essential
singularities, for which a version of the Casorati-Weierstrass Theorem is
proven.Comment: 25 pages, 1 figur
$L_p$-Theory of Type $1,1$-Operators

This is a continuation of recent work on the general definition of
pseudo-differential operators of type $1,1$, in H\"ormander's sense. Continuity
in $L_p$-Sobolev spaces and H\"older--Zygmund spaces, and more generally in
Besov and Lizorkin--Triebel spaces, is proved for positive smoothness, with
extension to arbitrary smoothness for operators in the self-adjoint subclass.
As a main tool the paradifferential decomposition is used for type
$1,1$-operators in combination with the Spectral Support Rule for
pseudo-differential operators and pointwise estimates in terms of maximal
functions of Peetre--Fefferman--Stein type.Comment: 18 pages. The accepted manuscript. (Final version appeared on 14
  September 2012 in Mathematische Nachrichten.
A necessary and sufficient condition on scattering for the regularly
  hyperbolic systems

The present paper is devoted to finding a necessary and sufficient condition
on the occurence of scattering for the regularly hyperbolic systems with
time-dependent coefficients whose time-derivatives are integrable over the real
line. More precisely, it will be shown that the solutions are asymptotically
free if the coefficients are stable in the sense of the Riemann integrability
as time goes to infinity, while each nontrivial solution is never
asymptotically free provided that the coefficients are not R-stable as times
goes to infinity. As a by-product, the scattering operator can be constructed.
It is expected that the results obtained in the present paper would be brought
into the study of the asymptotic behaviour of Kirchhoff systems.Comment: 16 page
BMO spaces related to Laguerre semigroups

For the system of Laguerre functions inline image we define a suitable BMO space from the atomic version of the Hardy space inline image considered by Dziubański in [7], where inline image is the maximal operator of the heat semigroup associated to that Laguerre system. We prove boundedness of inline image over a weighted version of that BMO, and we extend such result to other systems of Laguerre functions, namely inline image and inline image. To do that, we work with a more general family of weighted BMO-like spaces that includes those associated to all of the above mentioned Laguerre systems. In this setting, we prove that the local versions of the Hardy-Littlewood and the heat-diffusion maximal operators turn to be bounded over such family of spaces for inline image weights. This result plays a decisive role in proving the boundedness of Laguerre semigroup maximal operators.Fil: Harboure, Eleonor Ofelia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Santa Fe. Instituto de Matemática Aplicada "Litoral"; ArgentinaFil: Chicco Ruiz, Anibal Leonardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Santa Fe. Instituto de Matemática Aplicada "Litoral"; Argentin
Push forward measures and concentration phenomena

In this note we study how a concentration phenomenon can be transferred from one measure μ to a push-forward measure ν. In the first part, we push forward μ by a central projection, and obtain a concentration inequality in terms of the medians of the given norms (with respect to μ) and the Banach-Mazur distance between them. This approach is finer than simply bounding the concentration of the push forward measure in terms of the Banach-Mazur distance between K and L. As a consequence we show that any normed probability space with exponential type concentration is far (even in an average sense) from subspaces of l_p. The sharpness of this result is shown by considering the inline image spaces
On a necessary aspect for the Riesz basis property for indefinite
  Sturm-Liouville problems

In 1996, H. Volkmer observed that the inequality
\[(\int_{-1}^1\frac{1}{|r|}|f'|dx)^2 \le K^2
\int_{-1}^1|f|^2dx\int_{-1}^1\Big|\Big(\frac{1}{r}f'\Big)'\Big|^2dx \] is
satisfied with some positive constant $K>0$ for a certain class of functions
$f$ on $[-1,1]$ if the eigenfunctions of the problem \[ -y"=\lambda\,
r(x)y,\quad y(-1)=y(1)=0 \] form a Riesz basis of the Hilbert space
$L^2_{|r|}(-1,1)$. Here the weight $r\in L^1(-1,1)$ is assumed to satisfy
$xr(x)>0$ a.e. on $[-1,1]$.
  We present two criteria in terms of Weyl-Titchmarsh $m$-functions for the
Volkmer inequality to be valid. Using these results we show that this
inequality is valid if the operator associated with the spectral problem
satisfies the linear resolvent growth condition. In particular, we show that
the Riesz basis property of eigenfunctions is equivalent to the linear
resolvent growth if $r$ is odd.Comment: 26 page
Kolmogorov Equations for Randomly Perturbed Generalized Newtonian Fluids

We consider incompressible generalized Newtonian fluids in two space
dimensions perturbed by an additive Gaussian noise. The velocity field of such
a fluid obeys a stochastic partial differential equation with fully nonlinear
drift due to the dependence of viscosity on the shear rate. In particular, we
assume that the extra stress tensor is of power law type, i.\,e. a polynomial
of degree $p-1$, $p \in (1,2)$, i.\,e. the shear thinning case. We prove that
the associated Kolmogorov operator $K$ admits at least one infinitesimally
invariant measure $\mu$ satisfying certain exponential moment estimates.
Moreover, $K$ is $L^2$-unique w.\,r.\,t. $\mu$ provided $p \in (p^\ast,2)$,
where $p^\ast$ is the second root of $p^3 - 8p^2 + 14p -6 =0$, approximately
$p^\ast \approx 1.60407$.Comment: 16 page
Distributional representations of Nκ(∞) -functions

The subclasses Nκ(∞) of the classes Nκ of generalized Nevanlinna functions appear in the context of Pontryagin space models, where they correspond to model relations having a particular spectral behaviour. Applications are found, for instance, in the investigation of differential expressions with singular coefficients. We study representations of Nκ(∞)-functions as Cauchy-type integrals in a distributional sense and characterize the class of distributions occurring in such representations. We make explicit how the Pontryagin space model of an Nκ(∞)-function is related to the multiplication operator in the L2-space of the measure which describes the action of the representing distribution away from infinity. Moreover, we determine the distributional representations of a pair of functions associated with a symmetric generalized Nevanlinna function
Anisotropic Lizorkin--Triebel Spaces with Mixed Norms --- Traces on
  Smooth Boundaries

This article deals with trace operators on anisotropic Lizorkin--Triebel
spaces with mixed norms over cylindrical domains with smooth boundary. As a
preparation we include a rather self-contained exposition of Lizorkin--Triebel
spaces on manifolds and extend these results to mixed-norm Lizorkin--Triebel
spaces on cylinders in Euclidean space. In addition Rychkov's universal
extension operator for a half space is shown to be bounded with respect to the
mixed norms, and a support preserving right-inverse of the trace is given
explicitly and proved to be continuous in the scale of mixed-norm
Lizorkin--Triebel spaces. As an application, the heat equation is considered in
these spaces, and the necessary compatibility conditions on the data are
deduced.Comment: 35 pages. The accepted manuscript. (Final version appeared on 4 March
  2016 in Mathematische Nachrichten.
Left-symmetric algebroids

In this paper, we introduce a notion of a left-symmetric algebroid, which is
a generalization of a left-symmetric algebra from a vector space to a vector
bundle. The left multiplication gives rise to a representation of the
corresponding sub-adjacent Lie algebroid. We construct left-symmetric
algebroids from $\mathcal O$-operators on Lie algebroids. We study phase spaces
of Lie algebroids in terms of left-symmetric algebroids. Representations of
left-symmetric algebroids are studied in detail. At last, we study deformations
of left-symmetric algebroids, which could be controlled by the second
cohomology class in the deformation cohomology.Comment: 21 page
Scattering theory below energy for the cubic fourth-order
  Schr\"{o}dinger equation

We investigate the global existence and scattering for the cubic fourth-order
Schr\"{o}dinger equation $iu_t+\Delta^2u+|u|^2u=0$ in the low regularity space
$H^s(\R^n)$ with $s<2$. We provide an alternative approach to obtain a new
interaction Morawetz estimate and extend the range of the dimension of the
interactive estimate in Pausader \cite{P08} by modifying a tensor product
method appeared in \cite{CGT}. We combine interaction Morawetz estimates,
energy increments for the I-method to prove the result.Comment: 33page
On massive sets for subordinated random walks

We study massive (reccurent) sets with respect to a certain random walk
$S_\alpha $ defined on the integer lattice $\mathbb{Z} ^d$, $d=1,2$. Our random
walk $S_\alpha $ is obtained from the simple random walk $S$ on $\mathbb{Z} ^d$
by the procedure of discrete subordination. $S_\alpha $ can be regarded as a
discrete space and time counterpart of the symmetric $\alpha $-stable L\'{e}vy
process in $\mathbb{R}^d$.
  In the case $d=1$ we show that some remarkable proper subsets of $\mathbb{Z}$
, e.g. the set $\mathcal{P}$ of primes, are massive whereas some proper subsets
of $\mathcal{P}$ such as Leitmann primes $\mathcal{P}_h$ are
massive/non-massive depending on the function $h$. Our results can be regarded
as an extension of the results of McKean (1961) about massiveness of the set of
primes for the simple random walk in $\mathbb{Z}^3$.
  In the case $d=2$ we study massiveness of thorns and their proper subsets.Comment: 16 pages, 1 figur
The existence of light-like homogeneous geodesics in homogeneous
  Lorentzian manifolds

In previous papers, a fundamental affine method for studying homogeneous
geodesics was developed. Using this method and elementary differential topology
it was proved that any homogeneous affine manifold and in particular any
homogeneous pseudo-Riemannian manifold admits a homogeneous geodesic through
arbitrary point. In the present paper this affine method is refined and adapted
to the pseudo-Riemannian case. Using this method and elementary topology it is
proved that any homogeneous Lorentzian manifold of even dimension admits a
light-like homogeneous geodesic. The method is illustrated in detail with an
example of the Lie group of dimension 3 with an invariant metric, which does
not admit any light-like homogeneous geodesic
Comparison between overconvergent de Rham-Witt and crystalline cohomology for projective and smooth varieties

This is the  accepted  version  of  the  following  article: Comparison between overconvergent de Rham-Witt and crystalline cohomology for projective and smooth varieties, Early View (Online Version of Record published before inclusion in an issue) in Mathematische Nachrichten,  first published online 27 April 2015, which has been published in final form at http://dx.doi.org/10.1002/mana.201400220We prove that for a projective and smooth variety the hypercohomology of the overconvergent de Rham-Witt complex is canonically isomorphic to crystalline cohomolog
Lifting Galois sections along torsors

The cuspidalization conjecture, which is a consequence of Grothendieck's
section conjecture, asserts that for any smooth hyperbolic curve $X$ over a
finitely generated field $k$ of characteristic $0$ and any non empty Zariski
open $U \subset X$, every section of $\pi _1 (X, \bar x) \to \mathrm{Gal}_k$
lifts to a section of $\pi _1 (U,\bar x) \to \mathrm{Gal}_k$. We consider in
this article the problem of lifting Galois sections to the intermediate
quotient $ \pi_1^{cc}(U)$ introduced by Mochizuki. We show that when $k =
\mathbb Q$ and $D=X\setminus U$ is an union of torsion sub-packets every Galois
section actually lifts to $ \pi_1^{cc}(U)$. One of the main tools in the proof
is the construction of torus torsors $F_D$ and $E_D$ over $X$ and the geometric
interpretation $ \pi_1^{cc}(U) \simeq \pi _1 (F_D)$.Comment: v2 corresponds to the published, deeply revised and much shortened
  version. We think that v1, that contains the same results, could still be
  helpful to the reader preferring a self-contained tex
Functional calculus on real interpolation spaces for generators of
  $C_{0}$-groups

We study functional calculus properties of $C_{0}$-groups on real
interpolation spaces, using transference principles. We obtain interpolation
versions of the classical transference principle for bounded groups and of a
recent transference principle for unbounded groups. Then we show that each
group generator on a Banach space has a bounded $H^{\infty}_{1}$-calculus on
real interpolation spaces. Additional results are derived from this.Comment: Final version published in Mathematische Nachrichten, with some minor
  change
q-Differential equations for q-classical polynomials and q-Jacobi-Stirling numbers

We introduce, characterise and provide a combinatorial interpretation for the so-called q-Jacobi–Stirling numbers.\ud
This study is motivated by their key role in the (reciprocal) expansion of any power of a second order\ud
q-differential operator having the q-classical polynomials as eigenfunctions in terms of other even order operators,\ud
which we explicitly construct in this work. The results here obtained can be viewed as the q-version of\ud
those given by Everitt et al. and by the first author, whilst the combinatorics of this new set of numbers is a\ud
q-version of the Jacobi–Stirling numbers given by Gelineau and the second author
Well-posedness of non-autonomous linear evolution equations in uniformly
  convex spaces

This paper addresses the problem of wellposedness of non-autonomous linear
evolution equations $\dot x = A(t)x$ in uniformly convex Banach spaces. We
assume that $A(t):D \subset X\to X$, for each $t$ is the generator of a
quasi-contractive $C_0$-group where the domain $D$ and the growth exponent are
independent of $t$. Well-posedness holds provided that $t\mapsto A(t)y$ is
Lipschitz for all $y\in D$. H\"older continuity of degree $\alpha<1$ is not
sufficient and the assumption of uniform convexity cannot be dropped.Comment: 9 pages, to appear in Math. Nach
$(S+N)$-triangular operators: spectral properties and important examples

We introduce a notion of $(S+N)$-triangular operators in the Hilbert space
using some basic ideas from triangular representation theory. Our notion
generalizes the well-known notion of the spectral operators so that many
properties of the $(S+N)$-triangular operators coincide with those of spectral
operators. At the same time we show that wide classes of operators are
$(S+N)$-triangular.Comment: In this version of the paper, small misprints are removed, the style
  is improved and some references are adde
Skew-selfadjoint Dirac systems with rational rectangular Weyl functions:
  explicit solutions of direct and inverse problems and integrable wave
  equations

In this paper we study direct and inverse problems for discrete and
continuous time skew-selfadjoint Dirac systems with rectangular (possibly
non-square) pseudo-exponential potentials. For such a system the Weyl function
is a strictly proper rational rectangular matrix function and any strictly
proper rational matrix function appears in this way. In fact, extending earlier
results, given a strictly proper rational matrix function we present an
explicit procedure to recover the corresponding potential using techniques from
mathematical system and control theory. We also introduce and study a nonlinear
generalized discrete Heisenberg magnet model, extending earlier results for the
isotropic case. A large part of the paper is devoted to the related discrete
time systems of which the pseudo-exponential potential depends on an additional
continuous time parameter. Our techniques allows us to obtain explicit
solutions for the generalized discrete Heisenberg magnet model and evolution of
the Weyl functions