On elements of the Lax-Phillips scattering scheme for ρ-perturbations of an abstract wave equation

We give the definition of ρ-perturbations of an abstract wave equation. As a special case, this definition includes perturbations with compact support for the classical wave equation. By using the Lax-Phillips method, we study scattering of “ρ-perturbed” systems and establish some properties of corresponding scattering matrices.