This article is cited in 1 paper

On sets of absolute convergence for multiple trigonometric series

R. A. Avetisyan

M. V. Lomonosov Moscow State University

Abstract: We obtain a sufficient condition for a set of measure zero in $N$-dimensional space to be a set of absolute convergence (A. C. set) for an $N$-tuple trigonometric series. We also show that, in a certain subclass of sets of measure zero (namely in the subclass of ldquo monotonicrdquo curves), this condition cannot be sharpened.

UDC: 517.5

Received: 05.07.1972

 English version: Mathematical Notes, 1973, 13:5, 377–382

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