Distribution of complex transmission eigenvalues for spherically stratified media. (11th February 2015)

• Record Type: Journal Article
• Authors: Colton, David; Leung, Yuk-J; Meng, Shixu
• Is Part Of: Inverse problems. Volume 31:Number 3(2015:Mar.)
• Publication Date: 2015-02-11
• Subjects: inverse scattering -- complex transmission eigenvalues -- spectral theory; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/0266-5611/31/3/035006
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: In this paper, we employ transformation operators and Levinson's density formula to study the distribution of interior transmission eigenvalues for a spherically stratified media. In particular, we show that under smoothness condition on the index of refraction that there exist an infinite number of complex eigenvalues and there exist situations when there are no real eigenvalues. We also consider the case when absorption is present and show that under appropriate conditions there exist an infinite number of eigenvalues near the real axis.