Inverse problem of the spectral analysis for the Sturm-Liouville operator with non-separated boundary conditions and spectral parameter in the boundary condition

TL;DR

This paper addresses an inverse spectral problem for a Sturm-Liouville operator with non-separated boundary conditions involving a spectral parameter, establishing uniqueness, solvability conditions, and an algorithm using minimal spectral data.

Contribution

It introduces a new inverse problem framework for Sturm-Liouville operators with spectral parameter-dependent boundary conditions, providing a uniqueness theorem and solution method.

Findings

Proved a uniqueness theorem for the inverse problem.

Constructed a solution algorithm based on spectral data.

Established sufficient conditions for the inverse problem's solvability.

Abstract

This work deals with an inverse problem for the Sturm-Liouville operator with non-separated boundary conditions, one of which linearly depends on a spectral parameter. Uniqueness theorem is proved, solution algorithm is constructed and sufficient conditions for solvability of inverse problem are obtained. As spectral data, we only use the spectrum of one boundary value problem and some sequence of signs.