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Abstract <p>This work proves the existence of an integrable function <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(U(x)\)</EquationSource> <!--ContMath2670011Grigoryan-m1--> </InlineEquation> and a measurable set <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(E\subset[0,1)\)</EquationSource> <!--ContMath2670011Grigoryan-m2--> </InlineEquation> that form a universal pair <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\((\mathbf{U,E})\)</EquationSource> <!--ContMath2670011Grigoryan-m3--> </InlineEquation> in the sense of modification with respect to a multiplicative system.</p>

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On Fourier Series by Multiplicative Systems

  • 期刊论文

  • 发表日期：

    2026年6月20日

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  • M. G. Grigoryan,
  • L. S. Simonyan,
  • S. A. Sargsyan

摘要

Abstract

This work proves the existence of an integrable function \(U(x)\) and a measurable set \(E\subset[0,1)\) that form a universal pair \((\mathbf{U,E})\) in the sense of modification with respect to a multiplicative system.