Modified Lax–Phillips Scattering Theory

Abstract

As we have discussed in Chap. 2, several aspects of the Lax–Phillips scattering theory (Lax and Phillips 1967) distinguish it as an appealing abstract formalism for implementation even in situations outside of the strict range of problems for which it has been originally devised. The description of resonances in the framework of the Lax–Phillips theory possesses properties which may be considered as defining properties of an appropriate description of these objects. One such property is a dynamical characterization of resonances via their time evolution given in terms of a continuous, one parameter, strongly contractive semigroup, i.e., the Lax–Phillips semigroup. Specifically, resonances are identified as eigenvalues of the generator of the Lax–Phillips semigroup.