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Equipped absolutely continuous subspaces and stationary construction of the wave operators in the non-self-adjoint scattering theory

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Abstract

For a pair of non-self-adjoint operators with characteristic operator-functions having boundary values in the strong operator topology almost everywhere on the real axis, (local) wave operators are constructed. The investigation is based on the local stationary approach arising from the self-adjoint scattering theory and a certain interpretation of the absolutely continuous subspace as an equipped Hilbert space. Sufficient conditions for the existence of the wave operators are obtained and some of their properties are described. Bibliography:28 titles.

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Authors
  1. V. A. Ryzhov
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Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 217, 1994, pp. 144–171.

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Ryzhov, V.A. Equipped absolutely continuous subspaces and stationary construction of the wave operators in the non-self-adjoint scattering theory. J Math Sci 85, 1849–1866 (1997). https://doi.org/10.1007/BF02355295

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