Related papers: A Beurling-Lax-Halmos theorem for spaces with a co…

We prove multiplier theorems on rank one noncompact symmetric spaces which improve aspects of existing results. A common theme of our main results is that we partially drop specific assumptions on the multiplier function such as a…

For a collection of reproducing kernels k which includes those for the Hardy space of the polydisk and ball and for the Bergman space, k is a complete Pick kernel if and only if the multiplier algebra of the Hilbert space H^2(k) associated…

In 2016 and 2017, Haihui Fan, Don Hadwin and Wenjing Liu proved a commutative and noncommutative version of Beurling's theorems for a continuous unitarily invariant norm $\alpha $ on $L^{\infty}(\mathbb{T},\mu)$ and tracial finite von…

The aim of the present paper is three folds. For a reproducing kernel Hilbert space $\mathcal{A}$ (R.K.H.S) and a $\sigma-$finite measure space $(M_{1},d\mu_{1})$ for which the corresponding $L^{2}-$space is a separable Hilbert space, we…

We prove new kernel theorems for a general class of Beurling-Bj\"orck type spaces. In particular, our results cover the classical Beurling-Bj\"orck spaces $\mathcal{S}^{(\omega)}_{(\eta)}$ and $\mathcal{S}^{\{\omega\}}_{\{\eta\}}$ defined…

In this note it is shown that Berwald spaces admitting the same norm-preserving torsion-free affine connection have the same (weighted) Ricci curvatures. Combing this with Szab\'o's Berwald metrization theorem one can apply the…

We prove two new equivalences of the Feichtinger conjecture that involve reproducing kernel Hilbert spaces. We prove that if for every Hilbert space, contractively contained in the Hardy space, each Bessel sequence of normalized kernel…

We consider positive semidefinite kernels valued in the $*$-algebra of continuous and continuously adjointable operators on a VH-space (Vector Hilbert space in the sense of Loynes) and that are invariant under actions of $*$-semigroups. For…

We study integration and $L^2$-approximation in the worst-case setting for deterministic linear algorithms based on function evaluations. The underlying function space is a reproducing kernel Hilbert space with a Gaussian kernel of tensor…

We give a general inequality for Bergman kernels of Bergman spaces defined by convex weights in $\C^n$. We also discuss how this can be used in Nazarov's proof of the Bourgain-Milman theorem, as a substitute for H\"ormander's estimates for…

By making a seminal use of the maximum modulus principle of holomorphic functions we prove existence of $n$-best kernel approximation for a wide class of reproducing kernel Hilbert spaces of holomorphic functions in the unit disc, and for…

Sub-Bergman Hilbert spaces are analogues of de Branges-Rovnyak spaces in the Bergman space setting. They are reproducing kernel Hilbert spaces contractively contained in the Bergman space of the unit disk. K. Zhu analyzed sub-Bergman…

We give a simple proof of the Kernel theorem for the space of tempered ultradistributions of Beurling - Komatsu type, using the characterization of Fourier-Hermite coefficients of the elements of the space. We prove in details that the test…

This paper is devoted to the study of reproducing kernel Hilbert spaces. We focus on multipliers of reproducing kernel Banach and Hilbert spaces. In particular we tried to extend this concept and prove some theorems.

Let $\mathcal{E}$ be a Hilbert space and $H^2_{\mathcal{E}}(\mathbb{D})$ be the $\mathcal{E}$-valued Hardy space over the unit disc $\mathbb{D}$ in $\mathbb{C}$. The well known Beurling-Lax-Halmos theorem states that every shift invariant…

We introduce fusion, contragradient and braiding of Hilbert affine representations of a subfactor planar algebra $P$ (not necessarily having finite depth). We prove that if $N \subset M$ is a subfactor realization of $P$, then the Drinfeld…

We consider positive semidefinite kernels valued in the $*$-algebra of adjointable operators on a VE-space (Vector Euclidean space) and that are invariant under actions of $*$-semigroups. A rather general dilation theorem is stated and…

The invariant subspaces of the Hardy space on $H^2(\mathbb{D})$ of the unit disc are very well known however in several variables the structure of the invariant subspaces of the classical Hardy spaces is not yet fully understood. In this…

The famous Michael selection theorem deals with the characterisation of paracompact spaces by continuous selections of lower semi-continuous mappings in Banach spaces. In this paper, we will discuss several equivalent forms of this theorem,…

The universality properties of kernels characterize the class of functions that can be approximated in the associated reproducing kernel Hilbert space and are of fundamental importance in the theoretical underpinning of kernel methods in…