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

Abstract

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.