Related papers: The polyanalytic reproducing kernels
We demonstrate that a reproducing kernel Hilbert or Banach space of functions on a separable absolute Borel space or an analytic subset of a Polish space is separable if it possesses a Borel measurable feature map.
We show that every function in a reproducing kernel Hilbert space with a normalized complete Pick kernel is the quotient of a multiplier and a cyclic multiplier. This extends a theorem of Alpay, Bolotnikov and Kaptano\u{g}lu. We explore…
We introduce a $q$-deformation of the Fock space of holomorphic functions on $\mathbb{C}$, based on a geometric definition of $q$-analyticity. This definition is inspired by a standard construction in complex differential geometry. Within…
A classical result of Norbert Wiener characterises doubly shift-invariant subspaces for square integrable functions on the unit circle with respect to a finite positive Borel measure $\mu$, as being the ranges of the multiplication maps…
We consider the roots of uniformly chosen complex and real reciprocal polynomials of degree $N$ whose Mahler measure is bounded by a constant. After a change of variables this reduces to a generalization of Ginibre's complex and real…
We prove in a direct fashion that a multidimensional probability measure is determinate if the higher dimensional analogue of Carleman's condition is satisfied. In that case, the polynomials, as well as certain proper subspaces of the…
Herein, the theory of Bergman kernel is developed to the weighted case. A general form of weighted Bergman reproducing kernel is obtained, by which we can calculate concrete Bergman kernel functions for specific weights and domains.
Let $\mu$ be a positive finite measure on the unit circle. The Dirichlet type space $\mathcal{D}(\mu)$, associated to $\mu$, consists of holomorphic functions on the unit disc whose derivatives are square integrable when weighted against…
We introduce and study equivariant Hilbert series of ideals in polynomial rings in countably many variables that are invariant under a suitable action of a symmetric group or the monoid $Inc(\mathbb{N})$ of strictly increasing functions.…
Based on direct integrals, a framework allowing to integrate a parametrised family of reproducing kernels with respect to some measure on the parameter space is developed. By pointwise integration, one obtains again a reproducing kernel…
Let F(R^n) be the algebra of Fourier transforms of functions from L_1(R^n), K(R^n) be the algebra of Fourier transforms of bounded complex Borel measures in R^n and W be Wiener algebra of continuous 2pi-periodic functions with absolutely…
We develop a theory of Valuation Hilbert Modules and prove a version of Beurling's theorem for these. Then we apply our version of Beurling's theorem to obtain complete descriptions of the closed invariant subspaces of a number of Hilbert…
The halfspace depth of a $d$-dimensional point $x$ with respect to a finite (or probability) Borel measure $\mu$ in $\mathbb{R}^d$ is defined as the infimum of the $\mu$-masses of all closed halfspaces containing $x$. A natural question is…
The paper discusses a series of results concerning reproducing kernel Hilbert spaces, related to the factorization of their kernels. In particular, it is proved that for a large class of spaces isometric multipliers are trivial. One also…
If $\mu $ is a positive Borel measure on the interval $[0, 1)$ we let $\mathcal H_\mu $ be the Hankel matrix $\mathcal H_\mu =(\mu_{n, k})_{n,k\ge 0}$ with entries $\mu_{n, k}=\mu_{n+k}$, where, for $n\,=\,0, 1, 2, \dots $, $\mu_n$ denotes…
Let $X$ be a (real or complex) rearrangement-in\-va\-riant function space on $\Om$ (where $\Om = [0,1]$ or $\Om \subseteq \bbN$) whose norm is not proportional to the $L_2$-norm. Let $H$ be a separable Hilbert space. We characterize…
Motivated by applications to the study of stochastic processes, we introduce a new analysis of positive definite kernels $K$, their reproducing kernel Hilbert spaces (RKHS), and an associated family of feature spaces that may be chosen in…
We focus on Borel measures that have a globally subanalytic density function. We prove, given such a measure $\mu$ on a set $A$ and a globally subanalytic mapping $\Phi:A\to \Omega$, with $\Omega$ bounded open subset of $\mathbb{R}^n$, a…
We introduce new functional spaces that generalize the weighted Bergman and Dirichlet spaces on the disk D(0,R) in the complex plane and the Bargmann-Fock spaces on the whole complex plane. We give a complete description of the considered…
We proceed with studying the q-analogues of Cartan domains introduced in q-alg/9703005 and turn to the case of a ball in the space of complex matrices. An explicit expression for a positive $U_q\frak{su}_{nm}$-invariant integral (see…