Direct and inverse problems for the matrix Sturm-Liouville operator with\n the general self-adjoint boundary conditions

2020/06/11 by Natalia P. Bondarenko, Bondarenko, Natalia P. · 3 citations
Computer Science · Mathematics · #34A55 #34B09 #34B24 #34B45 #34L10 #34L20 #34L40 #FOS: Mathematics #Matrix Theory and Algorithms #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2006.06533

openalex publication_date 2020/06/11 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

The matrix Sturm-Liouville operator on a finite interval with the boundary\nconditions in the general self-adjoint form and with the singular potential\nfrom the class W₂^-1 is studied. This operator generalizes Sturm-Liouville\noperators on geometrical graphs. We investigate structural and asymptotical\nproperties of the spectral data (eigenvalues and weight matrices) of this\noperator. Furthermore, we prove the uniqueness of recovering the operator from\nits spectral data, by using the method of spectral mappings.\n

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• Stability of the inverse Sturm-Liouville problem on a quantum tree
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• Uniform stability for the matrix inverse Sturm-Liouville problems

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