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Abstract <p>In this paper it is proved that there exist universal pairs <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11982_2025_10505_Article_IEq1.gif" Format="GIF" Height="22" Rendition="HTML" Resolution="72" Type="Linedraw" Width="108" /> </InlineMediaObject> <EquationSource Format="TEX">\((\{ {{\lambda }_{{k,s}}}\} _{{k,s = 0}}^{\infty },E)\)</EquationSource> <!--RusMath2570049Grigoryan-m1--> </InlineEquation> in the sense of modification with respect to double multiplicative systems. A universal series with respect to the double Vilenkin system in the class of measurable functions of two variables is constructed.</p>

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On Universal Pairs Relative to the Vilenkin System

  • 期刊论文

  • 发表日期：

    2025年6月1日

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  • M. G. Grigoryan,
  • L. N. Galoyan,
  • T. M. Grigoryan

摘要

Abstract

In this paper it is proved that there exist universal pairs \((\{ {{\lambda }_{{k,s}}}\} _{{k,s = 0}}^{\infty },E)\) in the sense of modification with respect to double multiplicative systems. A universal series with respect to the double Vilenkin system in the class of measurable functions of two variables is constructed.