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Abstract <p> Spectral problems on the three-edge star graph with a Sturm–Liouville operator definedon each of the edges are studied. The spectral properties of such operators are analyzed; inparticular, asymptotic formulas for the eigenvalues and eigenfunctions of the operator with theDirichlet boundary conditions at the free ends and the continuity and Kirchhoff conditions at thecommon vertex are obtained. The potential in the Sturm–Liouville problem is assumed to besingular; namely, it is the derivative of a square integrable function in the sense of distributions.</p>

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Asymptotics of Eigenvalues and Eigenfunctions of the Sturm–Liouville Operator with a Singular Potential on a Star Graph: I

  • 期刊论文

  • 发表日期：

    2025年2月1日

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  • K. P. Zuev

摘要

Abstract

Spectral problems on the three-edge star graph with a Sturm–Liouville operator definedon each of the edges are studied. The spectral properties of such operators are analyzed; inparticular, asymptotic formulas for the eigenvalues and eigenfunctions of the operator with theDirichlet boundary conditions at the free ends and the continuity and Kirchhoff conditions at thecommon vertex are obtained. The potential in the Sturm–Liouville problem is assumed to besingular; namely, it is the derivative of a square integrable function in the sense of distributions.