The inverse spectral problem for transmission eigenvalues. (5th April 2017) - Cogar, Samuel; Colton, David; Leung, Yuk-J
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 .