Scattering in Other Wave Systems

Abstract

So far in this monograph we have been concerned with acoustic wave scattering problems. In dealing with such problems we have adopted the Wilcox theory of acoustic scattering introduced in [8]. The main reasons for doing this were, on the one hand, that the Wilcox theory uses quite elementary results from functional analysis, the spectral theory of self-adjoint operators on Hilbert spaces and semigroup theory and, on the other it leads quite readily to the development of constructive methods based on generalised eigenfunction expansion theorems. Furthermore, unlike the Lax-Phillips theory [2] the Wilcox theory applies to scattering problems in both even and odd space dimensions.