This article is cited in 3 papers

An example of a zero series expansion in the Walsh system

V. A. Skvortsov

M. V. Lomonosov Moscow State University

Abstract: We construct an example of a zero series expansion in the Walsh system which converges to zero outside some closed $M$ set of zero measure and converges to $+\infty$ at each point of this set. This shows, in particular, that in the theorem which says that a Walsh series which converges everywhere to a finite symmetric function is a Fourier series it is impossible to omit the requirement of finiteness and allow convergence of the series on a set of zero measure to an infinity of specified sign.

UDC: 517

Received: 05.02.1975

 English version: Mathematical Notes, 1976, 19:2, 108–112

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