We turn back to the well known problem of interpretation of the Schrodinger operator with
the pseudopotential being the first derivative of the Dirac function. We show that the problem …

We use the method of self‐adjoint extensions to define a self‐adjoint operator AT as the
singular perturbation of a given self‐adjoint operator A by a singular operator T on a Hilbert …

Rank-one perturbationsA α= A+ α (ϕ,·) ϕ of a semibounded selfadjoint operatorAare studied
with the help of distribution theory. It is shown that such perturbations can be defined for …

Gesztesy and Simon recently have proven the existence of the strong resolvent limit A∞, ω
for A α, ω= A+ α (· ω) ω, α→∞ where A is a self-adjoint positive operator, ω∈ H _-1 (H _s,\; s …

Rank one perturbations of selfadjoint operators which are not necessarily semibounded are
studied in the present paper. It is proven that such perturbations are uniquely defined, if they …

Norm resolvent approximation for a wide class of point interactions in one dimension is
constructed. To analyse the limit behaviour of Schrödinger operators with localized singular …

Let A be a symmetric restriction of a self-adjoint bounded from below operator A in a Hilbert
space'H and let Aoo denote the Friedrichs extension of A. We prove that in the case, where …

Approximations of rank one ${\mathcal H} _ {-2} $-perturbations of self-adjoint operators by
operators with regular rank one perturbations are discussed. It is proven that in the case of …

FINITE RANK PERTURBATIONS AND DISTRIBUTION THEORY 1. Introduction Finite rank
perturbations of selfadjoint operators are used in Page 1 PROCEEDINGS OF THE AMERICAN …

The negative eigenvalues problem for the generalized Laplace operator− Δ=− Δ++ αT, α< 0,
where T is a positive operator singular in L2 and acting from the Sobolev space W12 to its …