Abstract Lax-Phillips scattering scheme for second-order operator-differential equations - Kuzhel', S. A. (Ukrains’kyi Matematychnyi Zhurnal, 1996)
We construct an analog of the Lax-Phillips scattering scheme for an abstract operator-differential equation u u=-Lu under certain restrictions imposed on the operator L. In particular, we construct the incoming and outcoming subspaces and describe singularities of the scattering matrix in terms of the spaces of boundary values.