Inverse Indefinite Spectral Problem for Second Order Differential Operator with Complex Periodoc Coefficients

TL;DR

This paper investigates the inverse spectral problem for a Sturm-Liouville operator with complex periodic potential and discontinuous coefficients, establishing uniqueness and providing a constructive solution method.

Contribution

It introduces a new approach to solve the inverse problem for complex periodic potentials with discontinuities, including a uniqueness theorem and a constructive solution procedure.

Findings

Spectrum characterization of the operator

Uniqueness of the inverse problem solution

Constructive method for solving the inverse problem

Abstract

The inverse problem for the Sturm- Liouville operator with complex periodic potential and discontinuous coefficients on the axis is studied. Main characteristics of the fundamental solutions are investigated, the spectrum of the operator is studied. We give formulation of the inverse problem, prove a uniqueness theorem and provide a constructive procedure for the solution of the inverse problem.