This article is cited in 1 paper

On the Uniqueness Sets of Multiple Walsh Series for Convergence in Cubes

S. F. Lukomskii

Saratov State University

Abstract: Let $G^d$ be a power of the Cantor binary group $G$. The uniqueness problem for a multiple Walsh series on a power of the binary group in the case of convergence in cubes is discussed. It is proved that if $x\in G^{d-1}$, then $G\times \{x\}$ is the uniqueness set of a $d$-dimensional Walsh series in the case of convergence in cubes.

Keywords: multiple Walsh series, convergence in cubes, uniqueness set.

UDC: 517.51

Received: 14.07.2020
Revised: 26.10.2020

DOI: 10.4213/mzm12835

 English version: Mathematical Notes, 2021, 109:3, 427–434

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