\(L^ p\)-norm convergence of series in compact, totally disconnected groups
type: Item
instance of: scholarly article
title: \(L^ p\)-norm convergence of series in compact, totally disconnected groups
zbMATH Open document ID: 0856.42017
DOI: 10.1007/BF02342335
published in: Analysis Mathematica
publication date: 1996-09-18T00:00:00Z
review text: The authors study Fourier series on ``non-Abelian'' Vilenkin groups, i.e., totally disconnected, infinite compact groups whose topology satisfies a countability axiom. The main result is that when such a group is of bounded type, the Fourier series of any \(f\in L^p\), \(1\leq p\leq \infty\), is Cesàro summable to \(f\) in \(L^p\) norm. This generalizes the corresponding Abelian result which was obtained by \textit{J. Pál} and \textit{P. Simon} [Acta Math. Acad. Sci. Hung. 29, 155-164 (1977; Zbl 0345.42011)].
Mathematics Subject Classification ID: 42C10
Mathematics Subject Classification ID: 43A55
zbMATH DE Number: 913003
zbMATH Keywords: Walsh-Fourier series
zbMATH Keywords: Vilenkin groups
author: G. Gát
author: Rodolfo Toledo
reviewed by: William R. Wade
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 913003