About dependence of the Lax-Phillips scattering matrix on the choice of the incoming and outgoing subspaces (Q2754839)

In a series of papers the author has developed a version of the Lax-Phillips scattering theory for an abstract wave equation \(u_{tt}=-Lu\), where \(L\) is a positive self-adjoint operator on a Hilbert space \(H\) which is an extension of a symmetric operator \(B^2\). Here \(B\) is a simple maximal symmetric operator on a certain subspace \(H_0\subset H\). NEWLINENEWLINENEWLINEThe paper under review deals with dependence of the scattering matrix appearing in the above theory on the choice of the incoming and outgoing subspaces. It is known that for equivalent incoming or outgoing subspaces (the notion introduced by Lax and Phillips) the scattering matrices differ only by inessential factor. The author studies a more general case of quasi-equivalence, where the scattering matrices may have different singularities.