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Abstract <p> We consider Alexandrov’s<InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12002_2025_5130_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\(n\)</EquationSource> </InlineEquation>-width of the compact set of aperiodic<InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12002_2025_5130_Article_IEq3.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="28" /> </InlineMediaObject> <EquationSource Format="TEX">\(C^\infty\)</EquationSource> </InlineEquation>-smooth functions in a Gevrey class with<InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12002_2025_5130_Article_IEq4.gif" Format="GIF" Height="15" Rendition="HTML" Resolution="72" Type="Linedraw" Width="43" /> </InlineMediaObject> <EquationSource Format="TEX">\(\alpha \ge 1\)</EquationSource> </InlineEquation>. On the basis of a majorant of the<InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12002_2025_5130_Article_IEq5.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(k\)</EquationSource> </InlineEquation>th derivatives as<InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12002_2025_5130_Article_IEq6.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="57" /> </InlineMediaObject> <EquationSource Format="TEX">\(k\to \infty\)</EquationSource> </InlineEquation>, we find a lower estimate for the rate of decay of this<InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12002_2025_5130_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\(n\)</EquationSource> </InlineEquation>-width as<InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12002_2025_5130_Article_IEq8.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="58" /> </InlineMediaObject> <EquationSource Format="TEX">\(n\to \infty\)</EquationSource> </InlineEquation>.</p>

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On a Lower Estimate of Alexandrov’s \( n \)-Width of the Compact Set of Infinitely Smooth Aperiodic Functions in a Gevrey Class

  • 期刊论文

  • 发表日期：

    2025年9月1日

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  • V. N. Belykh

摘要

Abstract

We consider Alexandrov’s \(n\) -width of the compact set of aperiodic \(C^\infty\) -smooth functions in a Gevrey class with \(\alpha \ge 1\) . On the basis of a majorant of the \(k\) th derivatives as \(k\to \infty\) , we find a lower estimate for the rate of decay of this \(n\) -width as \(n\to \infty\) .