Convergence of multiple Fourier series for functions of bounded variation
type: Item
instance of: scholarly article
title: Convergence of multiple Fourier series for functions of bounded variation
zbMATH Open document ID: 0917.42015
DOI: 10.1007/BF02354993
published in: Mathematical Notes
publication date: 1999-01-11T00:00:00Z
review text: The pointwise convergence in Pringsheim's sense of multiple Fourier series of functions of bounded variation was proved by G. H. Hardy in 1906. In the present paper, the pointwise convergence of the partial sums of Fourier series is considered over a given sequence of bounded sets in the space of harmonics. Sufficient conditions are proved for the convergence, which are also necessary in the particular case when these sets are convex with respect to each coordinate direction.
Mathematics Subject Classification ID: 42B08
zbMATH DE Number: 1237999
zbMATH Keywords: pointwise convergence in Pringsheim's sense
zbMATH Keywords: multiple Fourier series
zbMATH Keywords: functions of bounded variation
author: S. A. Telyakovskiĭ
author: V. N. Temlyakov
reviewed by: Ferenc Móricz
MaRDI profile type: Publication
cites work: Q5800005
cites work: Some results on double Fourier series
cites work: Q3359161
cites work: Q3937799
description: scientific article; zbMATH DE number 1237999