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Abstract <p> This article is devoted to estimating the rate of equiconvergence of spectral expansions forthe Dirac system on a finite interval. The potential of the operator is assumed to be summable,and the boundary conditions are Birkhoff-regular. Results are obtained for the case where theexpanded function <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(f\)</EquationSource> </InlineEquation> is square summable, and qualified estimates of theequiconvergence rate are separately provided for the case of a square-summable potential and afunction <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(f\)</EquationSource> </InlineEquation> from the scale of Sobolev spaces.</p>

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On Estimates of the Rate of Equiconvergence of Spectral Expansions for the Dirac System with a Summable Potential

  • 期刊论文

  • 发表日期：

    2025年10月1日

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  • I. V. Sadovnichaya

摘要

Abstract

This article is devoted to estimating the rate of equiconvergence of spectral expansions forthe Dirac system on a finite interval. The potential of the operator is assumed to be summable,and the boundary conditions are Birkhoff-regular. Results are obtained for the case where theexpanded function \(f\) is square summable, and qualified estimates of theequiconvergence rate are separately provided for the case of a square-summable potential and afunction \(f\) from the scale of Sobolev spaces.