The Interior Transmission Eigenvalue Problem for Absorbing Media, in "Inverse Problems

Abstract. We consider the inverse problem of determining the spherically symmetric index of refraction n(r) from a knowledge of the corresponding transmission eigenvalues (which can be determined from field pattern of the scattered wave). We also show that for constant index of refraction n(r) = n, the smallest transmission eigenvalue suffices to determine n, complex eigenvalues exist for n sufficiently small and, for homogeneous media of general shape, determine a region in the complex plane where complex eigenvalues must lie. Key words. Interior transmission problem, transmission eigenvalues, inhomogeneous medium, inverse scattering. AMS subject classifications. 35R30, 35Q60, 35J40, 78A25. 1. Introduction. Th