Almost everywhere convergence of orthogonal series revisited
type: Item
instance of: scholarly article
title: Almost everywhere convergence of orthogonal series revisited
zbMATH Open document ID: 0820.42011
author: Ferenc Móricz
author: Károly Tandori
published in: Journal of Mathematical Analysis and Applications
publication date: 1995-07-20T00:00:00Z
review text: We deal with single and double orthogonal series and give sufficient conditions which ensure their convergence almost everywhere. Among others, we prove that if \[ \sum^ \infty_{j= 3} \sum^ \infty_{k= 3} a_{jk}^ 2\log j\log k\log^ 2_ +(1/a^ 2_{jk})<\infty, \] then the series \(\sum_ j\sum_ k a_{jk} \psi_{jk}(x)\) converges a.e. in Pringsheim's sense for each double orthonormal system \(\{\psi_{jk}(x)\}\). The interrelation between the well-known Rademacher-Menshov (type) theorems and ours are discussed in detail. At the end, we raise three problems concerning the characterization of a.e. convergence of orthogonal series.
reviewed by: Babu Ram
Mathematics Subject Classification ID: 42C15
zbMATH DE Number: 584079
zbMATH Keywords: measure space
zbMATH Keywords: rectangular partial sums
zbMATH Keywords: Rademacher-Menshov (type) theorems
zbMATH Keywords: double orthogonal series
zbMATH Keywords: almost everywhere convergence
MaRDI profile type: Publication
full work available at URL: jmaa.1994.1110
OpenAlex ID: W1976248084
DOI: 10.1006/JMAA.1994.1110
description: scientific article; zbMATH DE number 584079