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Abstract <p> Spectral problems on a star graph consisting of three edges with a Sturm–Liouvilleoperator defined on each of them are studied. We analyze the spectral properties of suchoperators; in particular, we obtain asymptotic formulas for the eigenvalues and eigenfunctions ofthe operator with the Dirichlet boundary conditions at the free ends and the continuity andKirchhoff conditions at the common vertex. The potential in the Sturm–Liouville problem isassumed to be singular; namely, it is the distributional derivative of a square integrable function.</p>

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

  • 期刊论文

  • 发表日期：

    2025年3月1日

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  • K. P. Zuev

摘要

Abstract

Spectral problems on a star graph consisting of three edges with a Sturm–Liouvilleoperator defined on each of them are studied. We analyze the spectral properties of suchoperators; in particular, we obtain asymptotic formulas for the eigenvalues and eigenfunctions ofthe operator with the Dirichlet boundary conditions at the free ends and the continuity andKirchhoff conditions at the common vertex. The potential in the Sturm–Liouville problem isassumed to be singular; namely, it is the distributional derivative of a square integrable function.