Transmission Eigenvalues and the Inverse Scattering Problem
David Colton

Abstract: We consider the scattering of time harmonic plane waves by an infinite dielectric cylinder. The subject of this talk is the inverse scattering problem of determining the cross section D of the cylinder and the relative permittivity of the dielectric from a knowledge of the far field pattern of the scattered wave. After a brief discussion of uniqueness and the analytic properties of the far field operator, we proceed to the determination of D by the linear sampling method and obtain a lower bound on the permittivity by the use of transmission eigenvalues. The transmission eigenvalue problem is a new class of spectral problems for partial differential equations which are particularly relevant in inverse scattering theory since transmission eigenvalues can be determined from the far field pattern. We will conclude the talk by a brief discussion of the special problems that occur when the medium is anisotropic.