Inverse Sturm-Liouville problems with summable potential

TL;DR

This paper characterizes the conditions under which given sequences can serve as eigenvalues and norming constants for Sturm-Liouville problems with real summable potentials, advancing inverse spectral theory.

Contribution

It provides necessary and sufficient conditions linking eigenvalues and norming constants to Sturm-Liouville problems with summable potentials.

Findings

Characterization of eigenvalues and norming constants for summable potentials

Necessary and sufficient conditions established

Advances inverse spectral problem understanding

Abstract

We describe the necessary and sufficient conditions for two sequences {\mu_n}^\infty_n=0 and {a_n}^\infty_n=0 to be correspondingly the set of eigenvalues and the set of norming constants of a Sturm-Liouville problem with real summable potential q and in advance fixed separated boundary conditions.