Uniform stability for the matrix inverse Sturm-Liouville problems

2025/06/18 by Natalia P. Bondarenko, Bondarenko, Natalia P. · 1 citation
Computer Science · Mathematics · #34A55 34B09 34B45 34L40 #Algebraic and Geometric Analysis #FOS: Mathematics #Matrix Theory and Algorithms #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2506.15300

openalex publication_date 2025/06/18 · openalex created_date 2025/10/19 · openalex updated_date 2026/07/28

Abstract

In this paper, the uniform stability of the inverse spectral problem is proved for the matrix Sturm-Liouville operator on a finite interval. Namely, we describe the sets of spectral data, on which the inverse spectral mapping is bounded and, consequently, the uniform estimates hold for the differences of the matrix potentials and of the corresponding coefficients of the boundary conditions. Our approach is based on a constructive procedure for solving the inverse problem by developing ideas of the method of spectral mappings. In addition, we apply our technique to obtain the uniform stability of the inverse Sturm-Liouville problem on the star-shaped graph.

Citations

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Cited by

• Stability of the inverse Sturm-Liouville problem on a graph with a cycle

Related

• Uniform stability of the inverse problem for the non-self-adjoint Sturm-Liouville operator
• Uniform stability for the inverse Sturm-Liouville problem with eigenparameter-dependent boundary conditions
• Uniform stability of the inverse Sturm-Liouville problem with polynomials in a boundary condition
• Inverse problems for Sturm--Liouville operators with potentials from Sobolev spaces. Uniform stability
• Spectral data characterization for the Sturm-Liouville operator on the\n star-shaped graph