Quasiperiodic inverse Sturm-Liouville problem

2025/07/28 by Bondarenko, Natalia P. · 1 citation
#34A55 34B09 34L40 #FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2507.20864

Abstract

In this paper, the Sturm-Liouville problem with nonseparated quasiperiodic boundary conditions is considered. We study the recovery of the problem parameters from the Hill-type discriminant, the Dirichlet spectrum, and the sequence of signs. We obtain the necessary and sufficient conditions of solvability, the local solvability and stability, as well as the uniform stability for this inverse spectral problem.

Citations

• On negative eigenvalues of 1D Schrödinger operators with δ'-like potentials
• On the uniform stability of recovering sine-type functions with asymptotically separated zeros
• Partial inverse problems for quadratic differential pencils on a graph\n with a loop
• Analyticity and uniform stability of the inverse singular\n Sturm--Liouville spectral problem
• Inverse problems for Sturm--Liouville operators with potentials from Sobolev spaces. Uniform stability
• Characterization of the spectrum of irregular boundary value problem for the Sturm-Liouville operator
• Inverse problems of spectral analysis for the Sturm-Liouville operator with regular boundary conditions

Cited by

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

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