Absolute convergence of Fourier series of functions of class Lip 1 and of functions of bounded variation
type: Item
instance of: scholarly article
zbMATH Open document ID: 1246.42004
published in: Izvestiya: Mathematics
publication date: 2012-06-08T00:00:00Z
Mathematics Subject Classification ID: 42A20
Mathematics Subject Classification ID: 42A16
Mathematics Subject Classification ID: 26A16
Mathematics Subject Classification ID: 26A45
zbMATH DE Number: 6043638
zbMATH Keywords: Fourier series
zbMATH Keywords: absolute convergence
zbMATH Keywords: orthonormal system
zbMATH Keywords: bounded variation
author: Vakhtang Tsagareishvili
MaRDI profile type: Publication
full work available at URL: im2012v076n02abeh002589
OpenAlex ID: W78465256
DOI: 10.1070/IM2012V076N02ABEH002589
title: Absolute convergence of Fourier series of functions of class Lip 1 and of functions of bounded variation
review text: If one does not restrict himself to the trigonometric system but considers a variety of orthonormal systems, certain interesting phenomena occur. On the one hand, Banach proved that given an \(L_2\) function, there is an orthonormal system with respect to which the Fourier series of this function diverges almost everywhere. On the other hand, the Fourier series with respect to a family of orthonormal systems of every function from Lip1 converges absolutely. This picture in whole differs from that for the trigonometric system alone. In the paper under review, the author distinguishes among all orthonormal systems those for which the Fourier series of every function from Lip1 converges absolutely. Functions of bounded variation are also studied in a similar way.
reviewed by: Elijah Liflyand
description: scientific article; zbMATH DE number 6043638