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Abstract <p>A homogeneous linear conjugate problem on a closed contour for a two-dimensional piecewise analytic vector is considered. Each solution to the problem is put in correspondence to a pair of functions, which are relations of limit values on the contour of the corresponding components of this solution. The relations are specified that couple the elements of the <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11982_2025_10485_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\(H\)</EquationSource> <!--RusMath2570029Kiyasov-m1--> </InlineEquation>-continuous matrix function of the problem, providing the existence of its two solutions, for which the corresponding components of the pair differ by rational multipliers, and the problem itself admits a solution in a closed form.</p>

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Efficient Factorization in Some Classes of Second-Order Hölder Matrix Functions

  • 期刊论文

  • 发表日期：

    2025年4月1日

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  • S. N. Kiyasov

摘要

Abstract

A homogeneous linear conjugate problem on a closed contour for a two-dimensional piecewise analytic vector is considered. Each solution to the problem is put in correspondence to a pair of functions, which are relations of limit values on the contour of the corresponding components of this solution. The relations are specified that couple the elements of the \(H\) -continuous matrix function of the problem, providing the existence of its two solutions, for which the corresponding components of the pair differ by rational multipliers, and the problem itself admits a solution in a closed form.