A new kind of uniqueness theorems for inverse Sturm-Liouville problems

TL;DR

This paper establishes new uniqueness theorems for inverse Sturm-Liouville problems, extending classical results and providing broader conditions under which the potential can be uniquely determined from spectral data.

Contribution

It introduces generalized Marchenko-type uniqueness theorems and extends Ambarzumyans theorem for inverse Sturm-Liouville problems, broadening the theoretical understanding.

Findings

Proved Marchenko-type uniqueness theorems

Generalized Ambarzumyans theorem

Enhanced conditions for potential recovery

Abstract

We prove Marchenko-type uniqueness theorems for inverse Sturm-Liouville problems. Moreover, we prove a generalization of Ambarzumyans theorem.