Bessel polynomial expansions in spaces of holomorphic functions
type: Item
instance of: scholarly article
title: Bessel polynomial expansions in spaces of holomorphic functions
zbMATH Open document ID: 0913.46003
author: M. Abul-Ez
published in: Journal of Mathematical Analysis and Applications
publication date: 1998-01-01T00:00:00Z
review text: Using abstract functional analytic methods, \textit{J. Cnops} and the author [Simon Stevin 67, No. 1-2, 145-156 (1993; Zbl 0814.46002)] proved a basis criterion for nuclear power series spaces \(K(\alpha, R)\); i.e., they gave necessary and sufficient conditions for an infinite matrix \(P\) such that, with \(e_k= (\delta_{nk})_n\), \(Pe\) is a basis of \(K(\alpha,R)\). In the present paper, the author discusses how this criterion leads to a refinement of the one of B. Cannon (1937) for spaces of holomorphic functions. He then utilizes it to derive that the sequence of Bessel polynomials is an effective basis in the space \({\mathcal O}(B(R))\) of holomorphic functions on the disk of radius \(R\), \(0<R<\infty\). -- There are some obvious misprints.
reviewed by: Klaus Dieter Bierstedt
Mathematics Subject Classification ID: 46A35
Mathematics Subject Classification ID: 46A11
Mathematics Subject Classification ID: 46E10
Mathematics Subject Classification ID: 46A04
zbMATH DE Number: 1215645
zbMATH Keywords: basis transform
zbMATH Keywords: polynomial basis
zbMATH Keywords: basis criterion
zbMATH Keywords: nuclear power series spaces
zbMATH Keywords: spaces of holomorphic functions
zbMATH Keywords: Bessel polynomials
zbMATH Keywords: effective basis
MaRDI profile type: Publication
full work available at URL: jmaa.1997.5840
OpenAlex ID: W2036899117
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DOI: 10.1006/JMAA.1997.5840
description: scientific article; zbMATH DE number 1215645