An Inverse Uniqueness in Interior Transmission Problem and Its Eigenvalue Tunneling in Penetrable Simple Domains

TL;DR

This paper investigates the inverse spectral problem in interior transmission problems within simple domains, using eigenvalue analysis and complex analysis techniques to establish uniqueness results related to the index of refraction.

Contribution

It introduces a novel approach by expanding solutions into one-dimensional problems and applying value distribution theory to eigenvalues for inverse spectral uniqueness.

Findings

Established inverse uniqueness based on spectral data.

Applied complex analysis to eigenvalue distribution.

Demonstrated eigenvalue tunneling in simple domains.

Abstract

We study an inverse uniqueness with a knowledge of spectral data in the interior transmission problem defined by an index of refraction in a simple domain. We expand the solution in such a domain into a series of one dimensional problems. For each one dimensional problem, we apply a value distribution theory in complex analysis to describe the eigenvalues of the system. By the orthogonality of the one dimensional system, we consider the uniqueness on the perturbation along each given incident angle.