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 Izv. Akad. Nauk SSSR Ser. Mat., 1977, Volume 41, Issue 3, Pages 703–716 (Mi izv1859)

On the rate of approach to zero of the coefficients of null series in the Haar and Walsh systems

V. A. Skvortsov

Abstract: The existence of null series in the Haar system with coefficients approaching zero at any prescribed rate admissible for such series is proved, and a class of null series in the Walsh system with coefficients tending to zero sufficiently rapidly is also constructed. It is proved that the series of squares of coefficients of a null series in the Walsh system may diverge arbitrarily slowly.
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English version:
Mathematics of the USSR-Izvestiya, 1977, 11:3, 665–676

Bibliographic databases:

UDC: 517.5
MSC: 42A56, 42A20

Citation: V. A. Skvortsov, “On the rate of approach to zero of the coefficients of null series in the Haar and Walsh systems”, Izv. Akad. Nauk SSSR Ser. Mat., 41:3 (1977), 703–716; Math. USSR-Izv., 11:3 (1977), 665–676

Citation in format AMSBIB
\Bibitem{Skv77} \by V.~A.~Skvortsov \paper On the rate of approach to zero of the coefficients of null series in the Haar and Walsh systems \jour Izv. Akad. Nauk SSSR Ser. Mat. \yr 1977 \vol 41 \issue 3 \pages 703--716 \mathnet{http://mi.mathnet.ru/izv1859} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=487244} \zmath{https://zbmath.org/?q=an:0376.42012|0384.42012} \transl \jour Math. USSR-Izv. \yr 1977 \vol 11 \issue 3 \pages 665--676 \crossref{https://doi.org/10.1070/IM1977v011n03ABEH001740} 

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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. Sh. T. Tetunashvili, “Trigonometric, Walsh, and Haar null-series”, Sb. Math., 187:3 (1996), 413–450
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