Singularly perturbed self-adjoint operators in scales of Hilbert spaces - Albeverio, S.; Kuzhel, S.; Nizhnik, L. (Український математичний журнал, 2007)
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 Schrodinger operator with generalized zero-range potential is considered in the Sobolev space Wp₂(R), p ∈ N.