Inverse Sturm-Liouville problems with fixed boundary conditions

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.