Weyl asymptotics of the transmission eigenvalues for a constant index of refraction

TL;DR

This paper establishes Weyl asymptotic formulas for transmission eigenvalues in a domain with constant refractive index, providing insights into their distribution for both real and complex cases.

Contribution

It presents the first Weyl asymptotics for transmission eigenvalues in a spherical domain with constant refractive index.

Findings

Weyl asymptotic formulas derived for transmission eigenvalues

Results apply to both real and complex eigenvalues

Provides a basis for spectral analysis in inverse scattering

Abstract

We prove Weyl type of asymptotic formulas for the real and the complex internal transmission eigenvalues when the domain is a ball and the index of refraction is constant.