Inverse Sturm-Liouville problems with fixed boundary conditions

TL;DR

This paper extends the characterization of spectral data for Sturm-Liouville problems by adding conditions that account for fixed boundary conditions, providing a complete necessary and sufficient criterion.

Contribution

It introduces two additional conditions to the spectral data characterization, enabling the description of Sturm-Liouville problems with fixed boundary conditions.

Findings

Added two conditions for spectral data with fixed boundary conditions

Provided necessary and sufficient criteria for spectral data

Extended classical results to fixed boundary condition cases

Abstract

Necessary and sufficient conditions for two sequences $\{\mu_n\}_{n=0}^\infty$ and $\{ a_n\}_{n=0}^\infty$ to be the spectral data for a certain Sturm-Liouville problem are well known. We add two more conditions so that the same two sequences become necessary and sufficient for being the spectral data for a Sturm-Liouville problem with fixed boundary conditions.