On the distribution of Born transmission eigenvalues in the complex plane

Article type: Research Article

Authors: Hovsepyan, Narek^{; *}

Affiliations: Department of Mathematics, Rutgers University, New Brunswick, NJ, USA

Correspondence: [*] Corresponding author. E-mail: [email protected].

Abstract: We analyze an approximate interior transmission eigenvalue problem in Rd 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.

Keywords: Born approximation, transmission eigenvalues, eigenvalue-free regions, inverse scattering, spherically stratified medium

DOI: 10.3233/ASY-231868

Journal: Asymptotic Analysis, vol. 136, no. 1, pp. 27-60, 2024