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 +∞ 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.
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Translated from Matematicheskie Zametki, Vol. 19, No. 2, pp. 179–186, February, 1976.
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Skvortsov, V.A. An example of a zero series expansion in the Walsh system. Mathematical Notes of the Academy of Sciences of the USSR 19, 108–112 (1976). https://doi.org/10.1007/BF01098741
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DOI: https://doi.org/10.1007/BF01098741