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 Mat. Zametki, 1976, Volume 19, Issue 2, Pages 179–186 (Mi mz7737)

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.

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

Bibliographic databases:

UDC: 517

Citation: V. A. Skvortsov, “An example of a zero series expansion in the Walsh system”, Mat. Zametki, 19:2 (1976), 179–186; Math. Notes, 19:2 (1976), 108–112

Citation in format AMSBIB
\Bibitem{Skv76} \by V.~A.~Skvortsov \paper An example of a~zero series expansion in the Walsh system \jour Mat. Zametki \yr 1976 \vol 19 \issue 2 \pages 179--186 \mathnet{http://mi.mathnet.ru/mz7737} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=410246} \zmath{https://zbmath.org/?q=an:0334.42019|0329.42011} \transl \jour Math. Notes \yr 1976 \vol 19 \issue 2 \pages 108--112 \crossref{https://doi.org/10.1007/BF01098741} 

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. A. A. Talalyan, R. I. Ovsepian, “The representation theorems of D. E. Men'shov and their impact on the development of the metric theory of functions”, Russian Math. Surveys, 47:5 (1992), 13–47
2. N. N. Kholshchevnikova, “On the category of $\mathcal U$-sets for series in the Walsh system”, Math. Notes, 53:5 (1993), 539–554
3. M. G. Grigoryan, “On an orthonormal system”, Russian Math. (Iz. VUZ), 46:4 (2002), 22–26
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