ABSTRACT
The scattering theory of Lax and Phillips brings together several branches of analysis to elucidate the rich structure of scattering of waves by a fixed obstacle. Walter Strauss and the author have developed a scattering theory which extends that of Lax and Phillips to include situations where the scattering obstacle is in motion. One approach has been to reformulate as much as possible of the Lax-Phillips framework in completely time dependent language. The chapter discusses some questions of energy conservation and decay. It provides an axiomatic discussion of the scattering operator S and the translation and spectral representations S# and S˜. The chapter is devoted to some final remarks about the case of periodic motion and the existence of scattering frequencies.
