Abstract
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.
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Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Institute im. V. A. Steklova Akademii Nauk SSSR, Vol. 178, pp. 92–119, 1989.
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Solomyak, B.M. Scattering theory for almost unitary operators, and a functional model. J Math Sci 61, 2002–2018 (1992). https://doi.org/10.1007/BF01095664
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DOI: https://doi.org/10.1007/BF01095664