Hypercyclicity of translation operators in a reproducing kernel Hilbert space of entire functions induced by an analytic Hilbert-space-valued kernel
type: Item
instance of: scholarly article
title: Hypercyclicity of translation operators in a reproducing kernel Hilbert space of entire functions induced by an analytic Hilbert-space-valued kernel
zbMATH Open document ID: 1447.47017
published in: Osaka Journal of Mathematics
publication date: 2015-10-30T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.ojm/1437137610
review text: In this article, the hypercyclicity of non-trivial translation operators in some general reproducing kernel Hilbert spaces of entire functions is studied. These spaces are obtained by duality in a complex separable Hilbert space \(\mathcal{H}\) by means of an analytic \(\mathcal{H}\)-valued kernel, namely, \(\mathcal{H}_K\). This space inherits the Hilbertian structure from \(\mathcal{H}\). The result is partially based on a result by \textit{K. C. Chan} and \textit{J. H. Shapiro} [Indiana Univ. Math. J. 40, No. 4, 1421--1449 (1991; Zbl 0771.47015)] that states the hypercyclicity from the density of the set of polynomials on \(\mathbb{C}\). In some cases, the space \(\mathcal{H}_K\) can be isometrically isomorphic to a de~Branges space where the set of polynomials is dense. Then, the hypercyclicity of the non-trivial translation operators can be stated. The results are illustrated with an example taken from Hamburger moment problem theory.
Mathematics Subject Classification ID: 47A16
Mathematics Subject Classification ID: 47B32
Mathematics Subject Classification ID: 42C15
zbMATH DE Number: 6502586
zbMATH Keywords: hypercyclity
zbMATH Keywords: translation operators
zbMATH Keywords: Hilbert spaces
zbMATH Keywords: reproducing kernel
zbMATH Keywords: de Branges theory
zbMATH Keywords: Hamburger moment problem
author: A. G. Garcia
author: M. A. Hernández-Medina
author: A. Portal
reviewed by: José Alberto Conejero
MaRDI profile type: Publication
cites work: Classification of security properties in a Linda-like process algebra
cites work: Q5539946
cites work: Q4007848
cites work: On Lagrange-type interpolation series and analytic Kramer kernels
cites work: The Zero-Removing Property and Lagrange-Type Interpolation Series
cites work: The discrete Kramer sampling theorem and indeterminate moment problems
cites work: On analytic sampling theory
cites work: Analytic Kramer kernels, Lagrange-type interpolation series and de Branges spaces
cites work: Operators with dense, invariant, cyclic vector manifolds
cites work: Geometry of Müntz spaces and related questions
cites work: Sequences of derivatives and normal families
cites work: Q4347099
cites work: The classical moment problem as a self-adjoint finite difference operator
description: scientific article; zbMATH DE number 6502586