Singularly perturbed self-adjoint operators in scales of Hilbert spaces

Abstract

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 $W_2^p(R),\quad p \in N$.