Scattering Theory for the Acoustic Wave Equation in an Arbitrary Exterior Domain

In this report the authors studied the spectral theory of the operator that is induced from problems in the n-dimensional Euclidean space either in the exterior domain or in the whole space for the hyperbolic linear partial-differential equations with the generalized Neumann boundary condition. The resulting theory provides a foundation for studying the wave operator and scattering operator involved in scattering theory and possibly also for studying the respective inverse problem.