This article is cited in 2 papers

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.
Bibliography: 6 titles.

UDC: 517.5

MSC: 42A56, 42A20

Received: 17.02.1976

 English version: Mathematics of the USSR-Izvestiya, 1977, 11:3, 665–676

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