On the distribution of Born transmission eigenvalues in the complex plane-Reference-Cited by-同舟云学术

On the distribution of Born transmission eigenvalues in the complex plane

Published:2023-12-08 Issue:1 Volume:136 Page:27-60
ISSN:1875-8576
Container-title:Asymptotic Analysis
language:
Short-container-title:ASY

Author:

Hovsepyan Narek¹

Affiliation:

1. Department of Mathematics, Rutgers University, New Brunswick, NJ, USA

Abstract

We analyze an approximate interior transmission eigenvalue problem in R d for d = 2 or d = 3, motivated by the transmission problem of a transformation optics-based cloaking scheme and obtained by replacing the refractive index with its first order approximation, which is an unbounded function. Using the radial symmetry we show the existence of (infinitely many) complex transmission eigenvalues and prove their discreteness. Moreover, it is shown that there exists a horizontal strip in the complex plane around the real axis, that does not contain any transmission eigenvalues.

Publisher

IOS Press

Subject

General Mathematics

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