Quasiperiodic inverse Sturm-Liouville problem

TL;DR

This paper investigates the inverse spectral problem for a quasiperiodic Sturm-Liouville operator, establishing conditions for solvability, stability, and reconstructing parameters from spectral data.

Contribution

It provides necessary and sufficient conditions for solving the inverse problem with quasiperiodic boundary conditions, including stability and solvability criteria.

Findings

Derived conditions for inverse problem solvability

Established stability and local solvability results

Analyzed spectral data for parameter recovery

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.