Singularly Perturbed Self-Adjoint Operators in Scales of Hilbert spaces

Details Singularly Perturbed Self-Adjoint Operators in Scales of Hilbert spaces Singularly Perturbed Self-Adjoint Operators in Scales of Hilbert spaces

2007-02-16

arxiv.org/abs/math-ph/0702057v1

Ukrainian Math. J. 59 (2007), no. 6, 787-810

Physics

Mathematical Physics

26 pages

Scientific paper

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}.

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