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Abstract <p>We have obtained an analogue of the Hochstadt–Lieberman theorem for the Sturm–Liouville operator on the half-axis with a complex-valued locally summable potential. Two cases are considered: a) the spectrum is discrete, b) the discrete spectrum has at least one finite limit point. Accordingly, two types of spectral data are presented, which ensure the uniqueness of the reconstruction of the potential specified on some half-line <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12202_2025_8402_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="117" /> </InlineMediaObject> <EquationSource Format="TEX">\((a,+\infty)\ (a&gt;0)\)</EquationSource> <!--LobJMat2560855Ishkin-m1--> </InlineEquation>.</p>

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Inverse Problem with Mixed Data for the Non-Self-Adjoint Sturm–Liouville Operator on the Half-Axis

  • 期刊论文

  • 发表日期：

    2025年7月1日

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  • Kh. Ishkin

摘要

Abstract

We have obtained an analogue of the Hochstadt–Lieberman theorem for the Sturm–Liouville operator on the half-axis with a complex-valued locally summable potential. Two cases are considered: a) the spectrum is discrete, b) the discrete spectrum has at least one finite limit point. Accordingly, two types of spectral data are presented, which ensure the uniqueness of the reconstruction of the potential specified on some half-line \((a,+\infty)\ (a>0)\) .