Inverse spectral problems for Sturm-Liouville operators with singular potentials, II. Reconstruction by two spectra

TL;DR

This paper presents a method for reconstructing singular potentials in Sturm-Liouville operators using two spectra, providing a complete algorithm and conditions for spectral data.

Contribution

It introduces a novel reconstruction algorithm for singular potentials from two spectra and establishes necessary and sufficient conditions for spectral data.

Findings

Reconstruction algorithm for singular potentials is developed.

Necessary and sufficient conditions for spectral data are provided.

The method applies to potentials in the space W^{-1}_2(0,1).

Abstract

We solve the inverse spectral problem of recovering the singular potentials $q\in W^{-1}_{2}(0,1)$ of Sturm-Liouville operators by two spectra. The reconstruction algorithm is presented and necessary and sufficient conditions on two sequences to be spectral data for Sturm-Liouville operators under consideration are given.