Singularly perturbed self-adjoint operators in scales of Hilbert spaces

  • S. A. Kuzhel'
  • L. P. Nizhnik


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 $W_2^p(R),\quad p \in N$.
How to Cite
Kuzhel’, S. A., and L. P. Nizhnik. “Singularly Perturbed Self-Adjoint Operators in Scales of Hilbert Spaces”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, no. 6, June 2007, pp. 723–743,
Research articles