Scattering theory for almost unitary operators, and a functional model

On the basis of a functional model one considers the scattering for operators that are close to unitary. In particular cases the presented scheme contains a series of results of L. de Branges and L. Shulman, S. N. Naboko, L. A. Sakhnovich, and H. Neidhardt. The fundamental new result is: the existence of complete local wave operators for a unitary operator and its nuclear perturbation, where the spectrum of the latter does not fill out the unit circle. In this same situation an invariance principle is obtained.