Weighted Banach spaces of entire functions
type: Item
instance of: scholarly article
title: Weighted Banach spaces of entire functions
zbMATH Open document ID: 0818.46025
DOI: 10.1007/BF01200439
author: Antonio Galbis
published in: Archiv der Mathematik
publication date: 1995-04-18T00:00:00Z
review text: It is proved that, given \(k> 0\) and \(p\in {\mathcal N}\), the Banach space \(E= H(e^{-k| z|^ p})_ 0({\mathcal C})\) of entire functions \(f\) such that \(| f(z)|= o(e^{k| z|^ p})\) is isomorphic to \(c_ 0\). An example of a rapidly decreasing continuous and radial weight \(v\) on \(\mathcal C\) such that the Banach space of entire functions \(f\) satisfying \(| f(z)|= o(v(z)^{-1})\) is not isomorphic to \(c_ 0\) is also included.
reviewed by: Antonio Galbis
Mathematics Subject Classification ID: 46E15
Mathematics Subject Classification ID: 46J15
Mathematics Subject Classification ID: 46B25
zbMATH DE Number: 743531
zbMATH Keywords: rapidly decreasing continuous and radial weight
zbMATH Keywords: Banach space of entire functions
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 743531