Abstract
Properties of the scattering operator and associated semigroup generated by the generalized Lax-Phillips scheme are studied. In particular, it is proved that the scattering operator admits decomposition into an orthogonal sum S=S1 ⊕ S2, where S1 is a unitary scattering operator in the sense of Lax-Phillips, S2 is a completely nonunitary operator of the type studied by C. Foias. For the associated semigroup T(t) up to the unitary component one gets the formula T(t)=T1(t) ⊕ T2(t), where T1(t) is the associated semigroup of class C00 and there exist subspaces such that a) The study of the structure of the original space and the properties of the operator S and of the semigroup T(t) let one decompose the scattering matrix into the orthogonal sum of pure and constant unitary parts.
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