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Abstract <p>The problem of the independence of subsystems of the Vilenkin–Chrestenson system, in particular, the Walsh one, is studied. A generalization of Borel’s theorem on the distribution of tuples of coefficients of expansions into an infinite <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11970_2025_7219_Article_IEq1.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(p\)</EquationSource> <!--BMatMGU2570043Kazakova-m1--> </InlineEquation>-ary fraction is also established.</p>

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On Subsystems of Independent Functions for Walsh and Vilenkin–Chrestenson Systems

  • 期刊论文

  • 发表日期：

    2025年6月1日

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  • A. D. Kazakova,
  • M. G. Plotnikov

摘要

Abstract

The problem of the independence of subsystems of the Vilenkin–Chrestenson system, in particular, the Walsh one, is studied. A generalization of Borel’s theorem on the distribution of tuples of coefficients of expansions into an infinite \(p\) -ary fraction is also established.