Cogar, Samuel; Colton, David; Leung, Yuk-J The inverse spectral problem for transmission eigenvalues. (English) Zbl 1372.35361 Inverse Probl. 33, No. 5, Article ID 055015, 15 p. (2017). Summary: 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 \(\eta\) 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 \(\eta\) whenever \(0<n(r)<\eta^2\) for \(0\leqslant r\leqslant 1\). Cited in 4 Documents MSC: 35R30 Inverse problems for PDEs 35P05 General topics in linear spectral theory for PDEs Keywords:inverse problem; transmission eigenvalues; refraction index; spherical symmetry PDFBibTeX XMLCite \textit{S. Cogar} et al., Inverse Probl. 33, No. 5, Article ID 055015, 15 p. (2017; Zbl 1372.35361) Full Text: DOI