Uniqueness for Inverse Sturm-Liouville Problems with a Finite Number of Transmission Conditions

TL;DR

This paper proves uniqueness theorems for inverse spectral problems involving Sturm-Liouville operators with finitely many interior discontinuities and transmission conditions, covering classical Robin and eigenparameter-dependent boundary conditions.

Contribution

It introduces new uniqueness results for inverse spectral problems with multiple interior discontinuities and various boundary conditions, extending previous work in the field.

Findings

Established uniqueness for inverse problems with multiple transmission points.

Extended results to include eigenparameter-dependent boundary conditions.

Provided comprehensive conditions ensuring spectral data determines the operator.

Abstract

We establish various uniqueness results for inverse spectral problems of Sturm-Liouville operators with a finite number of discontinuities at interior points at which we impose the usual transmission conditions. We consider both the case of classical Robin and of eigenparameter dependent boundary conditions.