A Density Theorem on the Eigenvalues of Spherically Symmetric Interior Transmission Problem in Absorbing Medium

TL;DR

This paper establishes a Weyl-type density theorem describing the asymptotic distribution of eigenvalues for the spherically symmetric interior transmission problem in absorbing media, using Cartwright's theory and asymptotic entire function techniques.

Contribution

It introduces a new density theorem for eigenvalues in absorbing media, extending previous results to spherically symmetric interior transmission problems.

Findings

Eigenvalues follow a Weyl-type asymptotic distribution.

Application of Cartwright's theory to transmission eigenvalue problems.

Development of a density theorem for eigenvalues in absorbing media.

Abstract

We describe the asymptotic distribution of the eigenvalues of interior transmission problem in absorbing medium. We apply the Cartwright's theory and the technique from asymptotic periodic entire function theory. We find a Weyl's type of density theorem on counting the eigenvalues for spherically symmetric interior transmission problem in absorbing medium.