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.