Singularly perturbed self-adjoint operators in scales of Hilbert spaces |
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Authors: | S Albeverio S Kuzhel’ L Nizhnik |
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Institution: | 1. Institut für Angewandte Mathematik, Universit?t Bonn, Bonn, Germany 2. Institute of Mathematics, Ukrainian National Academy of Sciences, Kyiv
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Abstract: | Finite-rank perturbations of a semibounded self-adjoint operator A are studied in a scale of Hilbert spaces associated with A. The notion of quasispace of boundary values is used to describe self-adjoint operator realizations of regular and singular perturbations of the operator A by the same formula. As an application, the one-dimensional Schrödinger operator with generalized zero-range potential is studied in the Sobolev space W 2 p (?), p ∈ ?. |
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