Related papers: Systems of reproducing kernels and their biorthogo…
We introduce a family of reproducing kernel Hilbert spaces $\mathcal A_\Lambda$ of holomorphic functions defined on an infinite--dimensional domain in a separable Hilbert space, $\mathbb{H}$. The reproducing kernel of $\mathcal A_\Lambda$…
In this paper we are concerned with the problem of completeness in the Bergman space of the worm domain $\mathcal{W}_\mu$ and its truncated version $\mathcal{W}'_\mu$. We determine some orthogonal systems and show that they are not…
This paper is devoted to the study of vector valued reproducing kernel Hilbert spaces. We focus on two aspects: vector valued feature maps and universal kernels. In particular we characterize the structure of translation invariant kernels…
It's well known that the functional Hilbert space over the unit ball in $B_{d} \in C^d$, with kernel function $K(z,w)=\frac{1}{1-z_{1}w_{1}-... -z_{d}w_{d}}$, admits a natural $A(B_{d})$-module structure. We show the rank of a nonzero…
We consider de Branges-Rovnyak spaces of a considerably large class of reproducing kernel Hilbert spaces and find a characterization for them to be complete Nevanlinna-Pick spaces. This extends as well as recovers earlier characterizations…
We generalize the orthonormal basis for the Gaussian RKHS described in \cite{MinhGaussian2010} to an infinite, continuously parametrized, family of orthonormal bases, along with some implications. The proofs are direct generalizations of…
We study how iterated and composed completely positive maps act on operator-valued kernels. Each kernel is realized inside a single Hilbert space where composition corresponds to applying bounded creation operators to feature vectors. This…
For a bounded linear operator $T$ acting on a reproducing kernel Hilbert space $\mathcal{H}(\Omega)$ over some non-empty set $\Omega$, the Berezin range and the Berezin radius of $T$ are defined respectively, by $\text{Ber}(T) := \{\langle…
We construct the coherent states in the sense of Gilmore and Perelomov for the fermionic Fock space. Our treatment is from the outset adapted to the infinite-dimensional case. The fermionic Fock space becomes in this way a reproducing…
In many instances one has to deal with parametric models. Such models in vector spaces are connected to a linear map. The reproducing kernel Hilbert space and affine- / linear- representations in terms of tensor products are directly…
In this note, we describe the backward shift invariant subspaces for a large class of reproducing kernel Hilbert spaces. This class includes in particular de Branges-Rovnyak spaces (the non-extreme case) and the range space of co-analytic…
The paper investigates the properties of certain biorthogonal polynomials appearing in a specific simultaneous Hermite-Pade' approximation scheme. Associated to any totally positive kernel and a pair of positive measures on the positive…
We obtain two results concerning the Feichtinger conjecture for systems of normalized reproducing kernels in the model subspace $K_\Theta = H^2\ominus \Theta H^2$ of the Hardy space $H^2$, where $\Theta$ is an inner function. First, we…
In this paper we study two separate problems on interpolation. We first give some new equivalences of Stout's Theorem on necessary and sufficient conditions for a sequence of points to be an interpolating sequence on a finite open Riemann…
The purpose of this work is to explore the existence and properties of reproducing kernel Hilbert subspaces of $L^2(\C, \, d^2z/\pi)$ based on subsets of complex Hermite polynomials. The resulting coherent states (CS) form a family…
We study reproducing kernel Hilbert spaces introduced as ranges of generalized Ces\`aro-Hardy operators, in one real variable and in one complex variable. Such spaces can be seen as formed by absolutely continuous functions on the positive…
We study the positive-definite completion problem for kernels on a variety of domains and prove results concerning the existence, uniqueness, and characterization of solutions. In particular, we study a special solution called the canonical…
We study the computational complexity of satisfiability problems for classes of simple finite height (ortho)complemented modular lattices $L$. For single finite $L$, these problems are shown tobe $\mc{NP}$-complete; for $L$ of height at…
It is well-known that the reproducing kernel of the space of spherical harmonics of fixed homogeneity is given by a Gegenbauer polynomial. By going over to complex variables and restricting to suitable bihomogeneous subspaces, one obtains a…
We introduce a complex-valued counterpart of the representer theorem in machine learning. We study several learning and minimization problems in reproducing kernel Hilbert spaces (RKHSs), with the aim of identifying appropriate input-output…