Example of a null-series with respect to periodic multiplicative systems
type: Item
instance of: scholarly article
title: Example of a null-series with respect to periodic multiplicative systems
zbMATH Open document ID: 0831.42019
DOI: 10.1007/BF01209079
author: N. A. Bokaev
author: M. A. Nurkhanov
published in: Mathematical Notes
publication date: 1995-09-12T00:00:00Z
review text: The authors consider the multiplicative Vilenkin orthonormal system \(\{\varphi_n(t): n= 0,1,\dots\}\) defined on a zero-dimensional compact Abelian group satisfying the second axiom of countability, and determined by the sequence \(\{p_n\}\) of primes. They construct an \(M\)-set of measure zero with respect to the system \(\{\varphi_n(t)\}\), without imposing any restriction on \(\{p_n\}\). As it is known, a set \(E\subset G\) is called an \(M\)-set with respect to \(\{\varphi_n(t)\}\) if there exists a series \(\sum a_n\varphi_n(t)\) with \(a_n\neq 0\) for at least one \(n\), which converges to zero everywhere outside \(E\). The construction follows in great lines that of the corresponding \(M\)-set for the Walsh system (when \(p_1= p_2=\cdots= 2\)).
Mathematics Subject Classification ID: 42C10
Mathematics Subject Classification ID: 43A75
zbMATH DE Number: 795646
zbMATH Keywords: multiplicative Vilenkin orthonormal system
zbMATH Keywords: \(M\)-set
zbMATH Keywords: Walsh system
reviewed by: Ferenc Móricz
MaRDI profile type: Publication
cites work: Q3715607
cites work: Q3881316
cites work: Q3729543
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description: scientific article; zbMATH DE number 795646