Part IV: Lax-Phillips theory
Abstract
The book Scattering theory by Lax and Phillips, appeared in 1960. It contains a spectral description of scattering by an obstacle. We describe it in a trivial case where there is no obstacle, so in a sense there is no scattering either, but we shall see that the Lax-Phillips construction is partly at the origin of the first conformal scattering construction, because in spite of its spectral nature, it connects the scattering data to the radiation field. In case people are not familiar with the notion of scattering, we shall also explain the general principle of a complete scattering theory, that is communication to all the various approaches one can find in the literature.