On the convergence of multiple Walsh-Fourier series of functions of bounded generalized variation
type: Item
instance of: scholarly article
title: On the convergence of multiple Walsh-Fourier series of functions of bounded generalized variation
zbMATH Open document ID: 1273.42029
DOI: 10.3103/S1068362312050020
published in: Journal of Contemporary Mathematical Analysis. Armenian Academy of Sciences
publication date: 2013-01-15T00:00:00Z
review text: The convergence of multiple Wash-Fourier series of functions of bounded generalized variation is investigated. Sufficient and necessary conditions on the sequence \(\lambda=\{\lambda_n\}\) are found for the convergence of multiple Walsh-Fourier series of functions of bounded partial \(\lambda\)-variation within the framework of continuous functions. The notation of \(\Lambda\)-variation was introduced by Waterman in 1972. Editorial remark: Theorem 1.1 of this paper and its proof coincide verbatim with Theorem 1.1 of [\textit{U. Goginava} and \textit{A. Sahakian}, Anal. Math. 39, No. 1, 45--56 (2013; Zbl 1299.42017)].
reviewed by: Enji Sato
Mathematics Subject Classification ID: 42C10
Mathematics Subject Classification ID: 42C05
Mathematics Subject Classification ID: 42C40
zbMATH DE Number: 6125667
zbMATH Keywords: Walsh-Fourier series
zbMATH Keywords: generalized variation
zbMATH Keywords: \(\lambda\)-variation
author: Ushangi Goginava
author: Artur Sahakian
MaRDI profile type: Publication
cites work: Continuity in $ \Lambda$-variation of functions of several variables and convergence of multiple Fourier series
cites work: Waterman classes and spherical partial sums of double Fourier series
cites work: Two-dimensional Waterman classes and $ u$-convergence of Fourier series
cites work: Convergence of double Fourier series and $W$-classes
cites work: Continuity in $ \Lambda$-variations of functions of several variables
cites work: On the convergence and divergence of multiple Fourier series with respect to the Walsh-Paley system in the spaces C and L
cites work: On the uniform convergence of multiple trigonometric Fourier series.
cites work: Uniform convergence of Cesàro means of negative order of double Walsh--Fourier series
cites work: On the uniform convergence of Walsh-Fourier series
cites work: On the convergence of double Fourier series of functions of bounded partial generalized variation
cites work: Q4756779
cites work: Rate of convergence for double Walsh-Fourier series of functions of bounded fluctuation
cites work: On the uniform convergence and L¹-convergence of double Walsh-Fourier series
cites work: Fourier series of functions of harmonic bounded fluctuation on groups
cites work: Q3805235
cites work: Q3997391
cites work: On convergence of Fourier series of functions of generalized bounded variation
cites work: Q3254471
cites work: Convergence and Gibbs phenomenon for double Fourier-Walsh series of functions of bounded harmonic variation
description: scientific article; zbMATH DE number 6125667