An inverse spectral uniqueness in exterior transmission problem

Abstract

We consider an inverse spectral theory in a domain with the cavity that is bounded by a penetrable inhomogeneous medium. An ODE system is constructed piecewise through the solutions inside and outside the cavity. The ODE system is connected to the PDE system via the analytic continuation. For each scattered angle, we describe its eigenvalue density in the complex plane, and prove an inverse uniqueness on the inhomogeneity by the measurements in the far-fields. MSC: 35Q60/35R30/34B24. Keywords: inverse scattering theory/inverse problem/Sturm-Liouville theory/exterior transmission problem/Cartwright-Levinson theory/spectral flaw of ODE.