On the uniform convergence of Walsh-Fourier series
type: Item
instance of: scholarly article
title: On the uniform convergence of Walsh-Fourier series
zbMATH Open document ID: 0992.42012
DOI: 10.1023/A:1013865315680
author: Ushangi Goginava
published in: Acta Mathematica Hungarica
publication date: 2002-06-25T00:00:00Z
review text: The generalized Wiener class BV\((p(n) \uparrow p)\) was introduced by \textit{H. Kita} and \textit{K. Yoneda} [Acta Math. Hung. 56, No. 3/4, 229-238 (1990; Zbl 0746.26007)]. In the present paper, the author finds necessary and sufficient conditions in terms of the modulus of continuity \(\omega\) which provide that for any function of the class \(H^{\omega} \bigcap \text{BV}(p(n) \uparrow \infty)\) the Walsh-Fourier series of the function converges to it uniformly on \([0,1]\).
Mathematics Subject Classification ID: 42C10
zbMATH DE Number: 1759088
zbMATH Keywords: Fourier series
zbMATH Keywords: Walsh system
zbMATH Keywords: uniform convergence
zbMATH Keywords: generalized Wiener class
reviewed by: Elena E. Berdysheva
MaRDI profile type: Publication
full work available at URL: a:1013865315680
OpenAlex ID: W1781487981
description: scientific article; zbMATH DE number 1759088