A uniqueness theorem on the eigenvalues of spherically symmetric interior transmission problem in absorbing medium

Abstract

We study the asymptotic distribution of the eigenvalues of interior transmission problem in absorbing medium. We apply Cartwright’s theory and the technique from entire function theory to find a Weyl’s type of density theorem in absorbing medium. Given a sufficient quantity of transmission eigenvalues, we obtain limited uniqueness on the refraction index as a uniqueness problem in entire function theory.

Keywords:

• absorbing media
• inverse problem
• transmission eigenvalue
• Cartwright theory
• almost periodic function
• spectral perturbation

MSC:

• 35P25
• 35R30
• 34B24

Acknowledgement

I want to thank the referee for an insightful report and many suggestions.