Related papers: On compact Hankel operators over compact Abelian g…

Let $D$ be an irreducible bounded symmetric domain with biholomorphism group $G$ with maximal compact subgroup $K$. For the Toeplitz operators with $K$-invariant symbols we provide explicit simultaneous diagonalization formulas on every…

For a $C^*$-algebra $A$ of compact operators and a compact manifold $M,$ we prove that the Hodge theory holds for $A$-elliptic complexes of pseudodifferential operators acting on smooth sections of finitely generated projective $A$-Hilbert…

Let $p>2$ be a prime number. In this short note, we calculate explicitly the unitary dual and the matrix coefficients of the Heisenberg group over the $p$-adic integers. As an application, we consider directional Vladimirov-Taibleson…

Let $(X, T^{1,0}X)$ be a connected orientable compact CR manifold of dimension $2n+1$, $n \geq 1$ with non-degenerate Levi curvature. In this paper, we study the algebra of Toeplitz operators on $X$ and we establish star product for some…

In this paper we consider Hankel operators on domains with bounded intrinsic geometry. For these domains we characterize the $L^2$-symbols where the associated Hankel operator is compact (respectively bounded) on the space of square…

We study compactness and the Fredholm property for linear operators on coorbit spaces over locally compact abelian phase spaces. In contrast to previous works, we do not impose any countability assumptions on the underlying groups. Our…

In this article, we propose a $p$-adic analogue of complex Hilbert space and consider generalizations of some well-known theorems from functional analysis and the basic study of operators on Hilbert spaces. We compute the $K$-theory of the…

Let ${\mathbb M}$ be an arbitrary o-minimal structure. Let $G$ be a definably compact definably connected abelian definable group of dimension $n$. Here we compute the new the intrinsic o-minimal fundamental group of $G;$ for each $k>0$,…

We study the Balmer spectrum of the category of finite G-spectra for a compact Lie group G, extending the work for finite G by Strickland, Balmer-Sanders, Barthel-Hausmann-Naumann-Nikolaus-Noel-Stapleton and others. We give a description of…

We introduce and investigate using Hilbert modules the properties of the {\em Fourier algebra} $A(G)$ for a locally compact groupoid $G$. We establish a duality theorem for such groupoids in terms of multiplicative module maps. This…

Carrier graphs of groups representing subgroups of a given relatively hyperbolic groups are introduced and a combination theorem for relatively quasi-convex subgroups is proven. Subsequently a theory of folds for such carrier graphs is…

A full subcategory of modules over a commutative ring $R$ is wide if it is abelian and closed under extensions. Hovey \cite{wide} gave a classification of wide subcategories of finitely presented modules over regular coherent rings in terms…

The usual Laurent expansion of the analytic tensors on the complex plane is generalized to any closed and orientable Riemann surface represented as an affine algebraic curve. As an application, the operator formalism for the $b-c$ systems…

Results of Liflyand and collaborators on the boundedness of Hausdorff operators on the Hardy space $H^1$ over finite-dimensional real space generalized to the case of locally compact groups that are spaces of homogeneous type. Special cases…

These are the lecture notes of a series of lectures on Dunkl operators. We discuss the underlying algebraic structure of the degenerate double affine Hecke algebra, intertwiners and shift operators. We apply this to Macdonald theory. We…

It is shown that a positive (bounded linear) operator on a Hilbert space with trivial kernel is unitarily equivalent to a Hankel operator that satisfies double positivity condition if and only if it is non-invertible and has simple spectrum…

We construct a large family of commutative algebras of partial differential operators invariant under rotations. These algebras are isomorphic extensions of the algebras of ordinary differential operators introduced by Grunbaum and Yakimov…

The bracket map was originally considered for locally compact abelian groups. In this work we extend the study of bracket maps to the noncommutative setting, providing characterizations of bases and frames for cyclic subspaces of the…

Using several complex variables techniques, we investigate the interplay between the geometry of the boundary and compactness of Hankel operators. Let f be a function smooth up to the boundary on a smooth bounded pseudoconvex domain D in…

(1) Every infinite, Abelian compact (Hausdorff) group K admits 2^|K|-many dense, non-Haar-measurable subgroups of cardinality |K|. When K is nonmetrizable, these may be chosen to be pseudocompact. (2) Every infinite Abelian group G admits a…