The inverse spectral problem for transmission eigenvalues. (5th April 2017)

• Record Type: Journal Article
• Authors: Cogar, Samuel; Colton, David; Leung, Yuk-J
• Is Part Of: Inverse problems. Volume 33:Number 5(2017:May)
• Publication Date: 2017-04-05
• Subjects: inverse scattering -- modified far field operator -- modified transmission eigenvalues; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/aa66d2
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: In this paper, we consider the inverse medium problem of determining the spherically stratified index of refraction n ( r ) from given spectral data. We begin by introducing a modified transmission eigenvalue problem depending on a parameter η and an associated modified far field operator. We prove that this operator is injective with dense range provided that k is not a modified transmission eigenvalue, and we show that n ( r ) is uniquely determined by the modified transmission eigenvalues corresponding to η whenever 0 < n ( r ) < η 2 for 0 ⩽ r ⩽ 1 .