An Uniqueness Result on Spherically Stratified Media with Interior Transmission Eigenvalues

TL;DR

This paper explores the relationship between transmission eigenvalues in spherically stratified media and entire function theory, revealing their inverse spectral properties and implications for uniqueness in inverse spectral problems.

Contribution

It establishes a connection between transmission eigenvalues and indicator functions in entire function theory, demonstrating their inverse spectral property for the first time.

Findings

Transmission eigenvalues relate to indicator functions in entire function theory.

The set of transmission eigenvalues exhibits an inverse spectral property.

The results imply uniqueness in inverse spectral problems for stratified media.

Abstract

Given a set of transmission eigenvalues, we describe the connection of such a set to the indicator functions in entire function theory. The indicator functions control the asymptotic growth rate of the solution of the Sturm-Liouville problem which has an uniqueness in the inverse spectral theory. Henceforth, the set of transmission eigenvalues has an inverse spectral property.