On Conditions for the Applicability of the Lax–Phillips Scattering Scheme to the Investigation of an Abstract Wave Equation - Kuzhel', S. A. (Ukrains’kyi Matematychnyi Zhurnal, 2003)
We find necessary and sufficient conditions under which orthogonal incoming and outgoing subspaces exist for a group of solutions of an abstract wave equation and possess an additional property of “equivalence” with respect to the operator of time reversion.