On an inverse problem for Sturm-Liouville equation

TL;DR

This paper establishes necessary and sufficient conditions for solving an inverse Sturm-Liouville problem with discontinuous coefficients and provides an algorithm for reconstructing the potential from spectral data.

Contribution

It introduces a new theorem on solvability conditions and presents an algorithm for potential reconstruction in Sturm-Liouville problems with discontinuities.

Findings

Proved a theorem on solvability conditions for the inverse problem.

Developed an algorithm for potential reconstruction from spectral data.

Enhanced understanding of inverse Sturm-Liouville problems with discontinuous coefficients.

Abstract

In this study, the theorem on necessary and sufficient conditions for the solvability of inverse problem for Sturm-Liouville operator with discontinuous coefficient is proved and the algorithm of reconstruction of potential from spectral data (eigenvalues and normalizing numbers) is given.