INV

Abstract

We consider the transmission eigenvalue problem for a spherically stratified medium and note that this eigenvalue problem is not self-adjoint. Nevertheless, considerable information on the the spectral theory of transmission eigenvalues can be obtained using methods from the theory of entire functions. In particular we will show that if the index of refraction is constant then complex eigenvalues exist and show that "most" of these complex eigenvalues lie near the real axis. We also consider the inverse spectral problem associated with this eigenvalue problem and show that that the solution of this problem depends heavily on whether or not the index of refraction is less than one or greater than one.