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Abstract <p> We study the basis properties of root functions of a <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10625_2025_2779_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="39" /> </InlineMediaObject> <EquationSource Format="TEX">\(2\times 2\)</EquationSource> </InlineEquation> Dirac operator with integrable complex-valuedpotential and irregular boundary conditions. Under certain conditions on the spectrum of theoperator, we prove that the root function system of this operator is incomplete in the space<InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10625_2025_2779_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="134" /> </InlineMediaObject> <EquationSource Format="TEX">\(L_2(0,\pi)\oplus L_2(0,\pi )\)</EquationSource> </InlineEquation> but forms an unconditionalbasis in the closed linear span of itself.</p>

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On the Properties of a Dirac Operator with Irregular Boundary Conditions

  • 期刊论文

  • 发表日期：

    2025年3月1日

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  • A. S. Makin

摘要

Abstract

We study the basis properties of root functions of a \(2\times 2\) Dirac operator with integrable complex-valuedpotential and irregular boundary conditions. Under certain conditions on the spectrum of theoperator, we prove that the root function system of this operator is incomplete in the space \(L_2(0,\pi)\oplus L_2(0,\pi )\) but forms an unconditionalbasis in the closed linear span of itself.