Abstract
We show that if a Walsh series whose coefficients tend towards zero is such that the subsequence of its partial sums indexed by nk, where nk satisfies the condition 2k−1<nk≤2k (k=0, 1, 2, ...), tends everywhere, except possibly for a denumerable set, towards a bounded functionf(x), then this series is the Fourier series of the functionf(x).
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Translated from Matematicheskie Zametki, Vol. 16, No. 1, pp. 27–32, July, 1974.
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Skvortsov, V.A. On the uniqueness of a Walsh series converging on subsequences of partial sum. Mathematical Notes of the Academy of Sciences of the USSR 16, 600–603 (1974). https://doi.org/10.1007/BF01098810
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DOI: https://doi.org/10.1007/BF01098810