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

2025/09/02 by Natalia P. Bondarenko, Bondarenko, Natalia P. · 1 citation
Mathematics · #34A55 34B09 34B45 34L40 #FOS: Mathematics #Graph theory and applications #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2509.02104

openalex publication_date 2025/09/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, the Sturm-Liouville operators on a graph with a cycle are considered. We study the inverse spectral problem, which consists in the recovery of the potentials from several spectra and a sequence of signs related to the quasiperiodic problem on the loop. The local stability of this inverse problem on the whole graph is proved. In addition, we investigate its uniform stability.

Citations

• An inverse problem on a metric graph with cycle
• Quasiperiodic inverse Sturm-Liouville problem
• Uniform stability for the matrix inverse Sturm-Liouville problems
• On negative eigenvalues of 1D Schrödinger operators with δ'-like potentials
• Uniform stability for the inverse Sturm-Liouville problem with eigenparameter-dependent boundary conditions
• Functional-differential operators on geometrical graphs with global delay and inverse spectral problems
• On the uniform stability of recovering sine-type functions with asymptotically separated zeros
• Constructive solution of the inverse spectral problem for the matrix\n Sturm-Liouville operator
• Uniform full stability of recovering convolutional perturbation of the\n Sturm-Liouville operator from the spectrum
• Partial inverse problems for quadratic differential pencils on a graph\n with a loop
• A partial inverse problem for the Sturm-Liouville operator on a star-shaped graph
• Inverse scattering problem for Sturm-Liouville operator on non-compact\n A-graph. Uniqueness result
• On an inverse problem for tree-like networks of elastic strings

Cited by

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

Related

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• A partial inverse problem for the Sturm-Liouville operator on a star-shaped graph
• Partial inverse problems for Sturm-Liouville operators on trees
• Uniqueness of Inverse Spectral Problem of Non-Local Sturm-Liouville Operators on Star Graph
• A partial inverse problem for the Sturm-Liouville operator on the graph with a loop