An Uniqueness Result on Spherically Stratified Media in Constant Absorbing Background with Interior Transmission Eigenvalues

TL;DR

This paper investigates how transmission eigenvalues in a constant absorbing medium uniquely determine the form of the functional determinant, utilizing Cartwright's theory in inverse problems.

Contribution

It establishes a uniqueness result linking transmission eigenvalues to the functional determinant in absorbing media, advancing inverse problem theory.

Findings

Density function inversely determines the indicator function

Asymptotic expansion of the functional determinant is uniquely determined

Application of Cartwright's theory to inverse problems in absorbing media

Abstract

Given a set of transmission eigenvalues, its density function inversely determines the form of the indicator function. This is one application of the Cartwright's theory in inverse problems. We use the indicator function inversely to determine the form of the functional determinant d(z). Such an asymptotic expansion is uniquely determined while considered in constant absorbing medium.