On the structure of divergence sets of Fourier-Walsh series
type: Item
instance of: scholarly article
title: On the structure of divergence sets of Fourier-Walsh series
zbMATH Open document ID: 0547.42013
DOI: 10.1007/BF02115870
author: S. Yu. Lukashenko
published in: Analysis Mathematica
publication date: 1984-01-01T00:00:00Z
review text: The author investigates the structure of the sets of divergence for some sequences of partial sums of Fourier series with respect to Walsh systems. It is proved that each set of \(G_{\delta}\) type on the dyadic group G is the set of unbounded divergence. In the class of sets of divergence for the continuous functions on G the sets which have sufficiently composite structure are indicated. Similar investigations for the trigonometrical Fourier series have been done earlier by the author [Vestn. Mosk. Univ., Ser. I 1978, No.2, 65-70 (1978; Zbl 0386.42002); ibid. 1982, No.3, 11-16 (1982; Zbl 0505.42007)].
Mathematics Subject Classification ID: 42C10
zbMATH DE Number: 3872013
zbMATH Keywords: sets of divergence
zbMATH Keywords: Walsh systems
zbMATH Keywords: set of \(G_{\delta}\) type
zbMATH Keywords: continuous functions
reviewed by: D. K. Ugulava
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3872013