On the uniqueness of a Walsh series converging on subsequences of partial sum

V. A. Skvortsov

M. V. Lomonosov Moscow State University, USSR

Abstract: We show that if a Walsh series whose coefficients tend towards zero is such that the subsequence of its partial sums indexed by $n_k$, where $n_k$ satisfies the condition $2^{k-1}<n_k\le2^k\quad(k=0,1,2,\dots)$, tends everywhere, except possibly for a denumerable set, towards a bounded function $f(x)$, then this series is the Fourier series of the function $f(x)$.

UDC: 517.5

Received: 14.02.1973

 English version: Mathematical Notes, 1974, 16:1, 600–603

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