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Abstract <p>The paper focuses on the Sturm–Liouville type differential equation with spectral boundary conditions defined over a finite interval. It employs the Hochstadt–Lieberman method alongside the Weyl function technique to get the potential on the interval <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\((0,\pi)\)</EquationSource> <!--LobJMat2560565Khalili-m1--> </InlineEquation> by a single spectrum, if the potential is given on the interval <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\left(0,\frac{\pi}{2}\right)\)</EquationSource> <!--LobJMat2560565Khalili-m2--> </InlineEquation>. Moreover, applying Gesztesy–Simon’s theorem and Weyl function technique, and knowing the potential on the interval <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\((0,\pi/2(1-\beta))\)</EquationSource> <!--LobJMat2560565Khalili-m3--> </InlineEquation> as <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\beta\in(0,1)\)</EquationSource> <!--LobJMat2560565Khalili-m4--> </InlineEquation>, a finite set of eigenvalues determines the potential on <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\((0,\pi)\)</EquationSource> <!--LobJMat2560565Khalili-m5--> </InlineEquation>.</p>

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On Uniqueness of Recovering of Sturm–Liouville Operators with the Spectral Boundary Condition

  • 期刊论文

  • 发表日期：

    2025年10月1日

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  • Yasser Khalili,
  • Nematollah Kadkhoda

摘要

Abstract

The paper focuses on the Sturm–Liouville type differential equation with spectral boundary conditions defined over a finite interval. It employs the Hochstadt–Lieberman method alongside the Weyl function technique to get the potential on the interval \((0,\pi)\) by a single spectrum, if the potential is given on the interval \(\left(0,\frac{\pi}{2}\right)\) . Moreover, applying Gesztesy–Simon’s theorem and Weyl function technique, and knowing the potential on the interval \((0,\pi/2(1-\beta))\) as \(\beta\in(0,1)\) , a finite set of eigenvalues determines the potential on \((0,\pi)\) .