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Article type: Research Article
Authors: Hovsepyan, Narek; *
Affiliations: Department of Mathematics, Rutgers University, New Brunswick, NJ, USA
Correspondence: [*] Corresponding author. E-mail: narek.hovsepyan@rutgers.edu.
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
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