Singularly Perturbed Self-Adjoint Operators in Scales of Hilbert spaces

S. Albeverio, S. Kuzhel, L. Nizhnik

Published 2007-02-16Version 1

Finite rank perturbations of a semi-bounded self-adjoint operator A are studied in the scale of Hilbert spaces associated with A. A concept of quasi-boundary value space is used to describe self-adjoint operator realizations of regular and singular perturbations of A by the same formula. As an application the one-dimensional Schr\"{o}dinger operator with generalized zero-range potential is considered in the Sobolev space W^p_2(\mathbb{R}), p\in\mathbb{N}.