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 p2 (ℝ), p ∈ ℕ.
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This issue is dedicated to the memory of Marko Hryhorovych Krein (04.03.1907–10.17.1989)
Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 6, pp. 723–743, June, 2007.
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Albeverio, S., Kuzhel’, S. & Nizhnik, L. Singularly perturbed self-adjoint operators in scales of Hilbert spaces. Ukr Math J 59, 787–810 (2007). https://doi.org/10.1007/s11253-007-0051-y
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DOI: https://doi.org/10.1007/s11253-007-0051-y