An inverse uniqueness on the index of refraction with a transition region

Abstract

The research focuses on an inverse eigenvalue problem in an interior transmission phenomenon. There is an asymptotic structure on the eigenvalues. Given a sufficient quantity of transmission eigenvalues, we prove an uniqueness on the index of refraction in some inhomogeneous medium as an uniqueness problem in entire function theory. Interior transmission eigenvalues are intersection points of two entire functions.

Keywords:

• inverse problem
• interior transmission eigenvalue
• value distribution theory
• transition point
• Cartwright-Levinson theory
• indicator diagram

AMS Subject Classifications:

• 35P25
• 35R30
• 34B24

Disclosure statement

No potential conflict of interest was reported by the author.