Inverse spectral problems for energy-dependent Sturm-Liouville equations

TL;DR

This paper addresses the inverse spectral problem for energy-dependent Sturm-Liouville equations, providing a complete spectral data description, a reconstruction algorithm, and proving uniqueness, by linking to Dirac operators.

Contribution

It introduces a novel approach connecting Sturm-Liouville and Dirac operators to solve inverse spectral problems for energy-dependent equations.

Findings

Complete spectral data characterization

Reconstruction algorithm proposed

Uniqueness of solution established

Abstract

We study the inverse spectral problem of reconstructing energy-dependent Sturm-Liouville equations from their Dirichlet spectra and sequences of the norming constants. For the class of problems under consideration, we give a complete description of the corresponding spectral data, suggest a reconstruction algorithm, and establish uniqueness of reconstruction. The approach is based on connection between spectral problems for energy-dependent Sturm-Liouville equations and for Dirac operators of special form.