Related papers: Berezin Kernels and Analysis on Makarevich Spaces

The article is devoted to the $q_R$-conformal modular functors, which being ``deformations'' of the conformal modular functor (the projective representation of the category $Train(Diff_+(S^1))$, the train of the group $Diff_+(S^1)$ of all…

We describe the symbolic calculus of operators on the unit sphere in the complex n-space $\mathbb C^n$ defined by the Berezin quantization. In particular, we derive a explicit formula for the composition of Berezin symbol and with that a…

We establish convolution inequalities for Besov spaces $B_{p,q}^s$ and Triebel--Lizorkin spaces $F_{p,q}^s$. As an application, we study the mapping properties of convolution semigroups, considered as operators on the function spaces…

The paper develops theory of covariant transform, which is inspired by the wavelet construction. It was observed that many interesting types of wavelets (or coherent states) arise from group representations which are not square integrable…

Let $P$ be a Markov kernel on a measurable space $\X$ and let $V:\X\r[1,+\infty)$. We provide various assumptions, based on drift conditions, under which $P$ is quasi-compact on the weighted-supremum Banach space $(\cB_V,\|\cdot\|_V)$ of…

Using the orthonormality of the 2D-Zernike polynomials, reproducing kernels, reproducing kernel Hilbert spaces, and ensuring coherent states attained. With the aid of the so-obtained coherent states, the complex unit disc is quantized.…

We define an involution on the space of compact tempered unipotent representations of inner twists of a split simple $p$-adic group $G$ and investigate its behaviour with respect to restrictions to reductive quotients of maximal compact…

In this paper, for n a positve integer, we compute the number of n degree representations for a dihedral group G of order 2m, m \geq 3 and the dimensions of the corresponding spaces of G invariant bilinear forms over a complex field C. We…

Francois Rodier proved that it is possible to view smooth representations of certain totally disconnected abelian groups (the underlying additive group of a finite-dimensional p-adic vector space, for example) as sheaves on the Pontryagin…

Given a locally compact quantum group $\mathbb G$, we study the structure of completely bounded homomorphisms $\pi:L^1(\mathbb G)\rightarrow\mathcal B(H)$, and the question of when they are similar to $\ast$-homomorphisms. By analogy with…

We prove approximation results about sequences of Berezin transforms of finite sums of finite product of Toeplitz operators (and bounded linear maps, in general) in the spirit of Ramadanov and Skwarczynski theorems that are about…

Since the results here have been superseded by another paper cowritten by the author, this article is available for reference purposes only. Fix a Dedekind domain $\mathcal{O}$ and a non-zero prime $\mathfrak{p}$ in it along with a…

The Weil representation of a real symplectic group $Sp(2n,R)$ admits a canonical extension to a holomorphic representation of a certain complex semigroup consisting of Lagrangian linear relations (this semigroup includes the Olshanski…

The Fredholm determinants of a special class of integral operators K supported on the union of m curve segments in the complex plane are shown to be the tau-functions of an isomonodromic family of meromorphic covariant derivative operators…

In this article, we consider flat and curved Riemannian symmetric spaces in the complex case and we study their basic integral kernels, in potential and spherical analysis: heat, Newton, Poisson kernels and spherical functions, i.e. the…

We introduce and study the Koszul complex for a Hecke $R$-matrix. Its cohomologies, called the Berezinian, are used to define quantum superdeterminant for a Hecke $R$-matrix. Their behaviour with respect to Hecke sum of $R$-matrices is…

Originally motivated by connections to integrable systems, two natural subalgebras of the rational Cherednik algebra have been considered in the literature. The first is the subalgebra of all degree zero elements and the second is the Dunkl…

We unify results of Artin, Brieskorn, Slodowy and others by showing that, in all characteristics, the Artin component of the deformation space of a rational surface singularity has a ramified cover where simultaneous resolution exists and…

Let $R$ be the homogeneous coordinate ring of the Grassmannian $\mathbb{G}=Gr(2,n)$ defined over an algebraically closed field $k$ of characteristic $p \geq \max\{n-2,3\}$. In this paper we give a description of the decomposition of $R$,…

This article describes how the ideas promoted by the fundamental papers published by M. Frazier and B. Jawerth in the eighties have influenced subsequent developments related to the theory of atomic decompositions and Banach frames for…