This article is cited in 1 paper

Example of a Divergent Fourier Series in the Vilenkin System

I. V. Polyakov

M. V. Lomonosov Moscow State University

Abstract: We construct an example of a function from the class $Lo(\sqrt{\ln^+L})$ whose Fourier–Vilenkin series diverges almost everywhere.

Keywords: Fourier series, Vilenkin system, Walsh system, Vilenkin function, Dirichlet kernel, Rademacher function.

UDC: 517.5

Received: 05.11.2009
Revised: 10.11.2010

DOI: 10.4213/mzm8607

 English version: Mathematical Notes, 2011, 89:5, 734–740

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