Hadamard multipliers on spaces of holomorphic functions
type: Item
instance of: scholarly article
title: Hadamard multipliers on spaces of holomorphic functions
zbMATH Open document ID: 1384.30013
author: Maria Trybuła
published in: Integral Equations and Operator Theory
publication date: 2017-11-10T00:00:00Z
review text: Motivated by the work [\textit{M. Langenbruch} and \textit{P. Domański}, Analysis, München 32, No. 2, 137--162 (2012; Zbl 1288.46020)] where the problem of multipliers is considered on spaces of real analytic functions, the present paper is devoted to the study of Hadamard multipliers on spaces of holomorphic functions. The aim of the paper is to find a representation of all multipliers on \(H(\Omega)\) where \(\Omega\) is a Runge open set from \(\mathbb C\). The paper is organized in six sections, the first one presenting the main notations and results. Also here some examples of Hadamard multiplication operators and Euler differential operators are presented. In the second section the properties of the dilation set \(V(\Omega)\) of \(\Omega\) are analyzed, and in the third one the topology on \(H(V)\) and its dual is studied. The main representation theorems, presented in the first section, are proved in the fourth section, obtaining a description of all Hadamard multipliers on \(H(\Omega)\) via analytic functionals \(H(V(\Omega))'\) on the space of holomorphic germs on the dilation of \(\Omega\). The continuity problems are analyzed in the fifth section, and in the last section of the paper some remarks and comments on the obtained results are presented. Also, equivalent assertions for an Euler differential operator (Theorem 6.3) are proved.
reviewed by: Ilie Valuşescu
Mathematics Subject Classification ID: 30H99
zbMATH DE Number: 6805235
zbMATH Keywords: spaces of holomorphic functions
zbMATH Keywords: Hadamard multipliers
zbMATH Keywords: analytic functionals
Wikidata QID: Q59608325
MaRDI profile type: Publication
full work available at URL: s00020-017-2369-7
OpenAlex ID: W2609436889
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DOI: 10.1007/S00020-017-2369-7
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description: scientific article; zbMATH DE number 6805235