Weighted vector-valued holomorphic functions on Banach spaces
type: Item
instance of: scholarly article
title: Weighted vector-valued holomorphic functions on Banach spaces
zbMATH Open document ID: 1300.46032
DOI: 10.1155/2013/501592
author: Enrique Jordá
published in: Abstract and Applied Analysis
publication date: 2014-06-23T00:00:00Z
review text: The purpose of this paper is to investigate conditions to ensure when a weakly holomorphic vector-valued function defined on a non void open and connected subset \(U\) of an infinite-dimensional Banach space \(X\) satisfying certain estimates is in fact holomorphic, and to give extension results for functions in a Banach space of holomorphic functions defined also on a non void open and connected \(U\) subset of \(X\). These investigations continue recent work by Arendt, Nikolski, Grosse-Erdmann, Frerick, Wengenroth, the author and the reviewer, among others. Extensions of theorems from Frerick, Jordá and Wengenroth in [\textit{L. Frerick} et al., Math. Nachr. 282, No. 5, 690--696 (2009; Zbl 1177.46024)] are obtained. Linearization of Banach spaces of vector-valued holomorphic functions constitutes an important technique in the paper. Several nice results and examples about different weighted Banach spaces of holomorphic functions defined on subsets of a Banach space \(X\) are given. They clarify the assumptions of the theorems given in the article.
reviewed by: José Bonet
Mathematics Subject Classification ID: 46E40
Mathematics Subject Classification ID: 46E15
Mathematics Subject Classification ID: 46G20
zbMATH DE Number: 6306943
zbMATH Keywords: weighted Banach spaces of holomorphic functions
zbMATH Keywords: infinite-dimensional holomorphy
zbMATH Keywords: weakly holomorphic functions
zbMATH Keywords: linearization
zbMATH Keywords: norming sets
Wikidata QID: Q58916918
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/501592
OpenAlex ID: W2011472460
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description: scientific article; zbMATH DE number 6306943