Related papers: Analytic and arithmetic properties of the $(\Gamma…
In this investigation of character tables of finite groups we study basic sets and associated representation theoretic data for complementary sets of conjugacy classes. For the symmetric groups we find unexpected properties of characters on…
In this paper, we give an integral representation for the boundary values of derivatives of functions of the de Branges--Rovnyak spaces $\HH(b)$, where $b$ is in the unit ball of $H^\infty(\CC_+)$. In particular, we generalize a result of…
We provide a new representation of a refinable shift invariant space with a compactly supported generator, in terms of functions with a special property of homogeneity. In particular these functions include all the homogeneous polynomials…
We develop a functorial framework for the ideal theory of commutative semirings using coherent frames and spectral spaces. Two central constructions-the radical ideal functor and the $k$-radical ideal functor-are shown to yield coherent…
One object of interest in random matrix theory is a family of point ensembles (random point configurations) related to various systems of classical orthogonal polynomials. The paper deals with a one--parametric deformation of these…
For a Reproducing Kernel Hilbert Space on a complex domain we give a formula that describes the Hermitean metrics on the domain which are pull-backs of some metric on the (dual of) the RKHS via the evaluation map. Then we consider the…
We consider the well-known Rosenbloom-Tsfasman function field lattices in the special case of Hermitian function fields. We show that in this case the resulting lattices are generated by their minimal vectors, provide an estimate on the…
This paper studies rational functions $\mathfrak{J}_\alpha(q)$, which depend on a positive element $\alpha$ of the root lattice of a root system. These functions arise as Shapovalov pairings of Whittaker vectors in Verma modules of highest…
Given the reproducing kernel $k$ of the Hilbert space $\mathcal{H}_k$ we study spaces $\mathcal{H}_k(b)$ whose reproducing kernel has the form $k(1-bb^*)$, where $b$ is a row-contraction on $\mathcal{H}_k$. In terms of reproducing kernels…
We study zeta functions enumerating finite-dimensional irreducible complex linear representations of compact p-adic analytic and of arithmetic groups. Using methods from p-adic integration, we show that the zeta functions associated to…
We review definitions and properties of reproducing kernel Hilbert spaces attached to Gaussian variables and processes, with a view to applications in nonparametric Bayesian statistics using Gaussian priors. The rate of contraction of…
The theory of Ihara zeta functions is extended to non-compact arithmetic quotients of Bruhat-Tits trees. This new zeta function turns out to be a rational function, despite the infinite-dimensional setting. In general it has zeros and…
The Wigner function of a dynamical infinite dimensional lattice is studied. A closed differential equation without diffusion terms for this function is obtained and solved. We map atom-photon interaction systems, such as the Jaynes-Cummings…
This is a continuation of our "Lecture on Kac--Moody Lie algebras of the arithmetic type" \cite{25}. We consider hyperbolic (i.e. signature $(n,1)$) integral symmetric bilinear form $S:M\times M \to {\Bbb Z}$ (i.e. hyperbolic lattice),…
The Bessmertny\u{\i} class consists of rational matrix-valued functions of $d$ complex variables representable as the Schur complement of a block of a linear pencil $A(z)=z_1A_1+\cdots+z_dA_d$ whose coefficients $A_k$ are positive…
For any Hermitian Lie group G of tube type we construct a Fock model of its minimal representation. The Fock space is defined on the minimal nilpotent K_C-orbit X in p_C and the L^2-inner product involves a K-Bessel function as density.…
This paper is concerned with the well-posedness analysis of the Hartree-Fock system modeling the time evolution of a quantum system comprised of fermions. We consider quantum states with finite mass and finite kinetic energy, and the…
We obtain a family of matrix integrals which decompose to a product of Gamma-functions (they have some relations with S.G.Gindikin 'Beta', but generally speaking essentially differ from it). We obtain Plancherel formula for Berezin…
We prove that the Bergman kernel function associated to a finitely connected domain in the plane is given as a rational combination of only three basic functions of one complex variable: an Alhfors map, its derivative, and one other…
For the space $Lat_n$ of all the lattices in a $p$-adic $n$-dimensional linear space we obtain an analog of matrix beta-functions; this beta-function has a degeneration to the Tamagawa zeta-function. We propose an analog of Berezin kernels…