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Abstract <p> We show that <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11006_2025_3105_Article_IEq2.gif" Format="GIF" Height="22" Rendition="HTML" Resolution="72" Type="Linedraw" Width="178" /> </InlineMediaObject> <EquationSource Format="TEX">\(d_n(W^1_1,L_q)\asymp n^{-1/2}\log n\)</EquationSource> </InlineEquation> for <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11006_2025_3105_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="82" /> </InlineMediaObject> <EquationSource Format="TEX">\(2&lt;q&lt;\infty\)</EquationSource> </InlineEquation>. This completes the solution of the problem on orders of decay of the Kolmogorov widths in the classical case of Sobolev classes of integer smoothness on an interval. </p>

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Kolmogorov Widths of the Class \(W_1^1\)

  • 期刊论文

  • 发表日期：

    2025年6月1日

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  • Yu. V. Malykhin

摘要

Abstract

We show that \(d_n(W^1_1,L_q)\asymp n^{-1/2}\log n\) for \(2<q<\infty\) . This completes the solution of the problem on orders of decay of the Kolmogorov widths in the classical case of Sobolev classes of integer smoothness on an interval.