Properties of the far field operator in the inverse conductive scattering problem

In this paper, we have studied the properties of the far field operator in the inverse scattering problem with the conductive boundary condition. The far field operator which maps the boundary data into the far field pattern of the solution to a boundary value problem plays a fundamental role in inverse scattering theory. In scattering theory the boundary data are given by the traces of plane waves. We have characterized the closure of the image in L2 space under the far field operator of the span of the traces of these incident plane waves.