Abstract
Finite rank generalized singular perturbations of selfadjoint operators are studied. It is proved that the restriction of the arising operator relation to the subspace generated by the original Hilbert space is a selfadjoint operator (if the perturbation is singular). The relations with the corresponding scattering problem are investigated. In particular, the case where the scattering matrix has physical behavior at infinity is examined.
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Kurasov, P., Pavlov, B. (2000). Scattering Problem with Physical Behavior of Scattering Matrix and Operator Relations. In: Havin, V.P., Nikolski, N.K. (eds) Complex Analysis, Operators, and Related Topics. Operator Theory: Advances and Applications, vol 113. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8378-8_16
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DOI: https://doi.org/10.1007/978-3-0348-8378-8_16
Publisher Name: Birkhäuser, Basel
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