We review recent developments in the theory of 1-D Schrödinger operators with local point
interactions on a discrete set. The progress in this area was stimulated by recent advances …

We study the Hamiltonians HX, α, q with δ-type point interactions at the centers xk on the
positive half line in terms of energy forms. We establish analogs of some classical results on …

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 …

We are going to consider the M. Kreĭn classical papers on the theory of semi-bounded
operators and the theory of contractive self-adjoint extensions of Hermitian contractions, and …

Schrödinger operators with singular potentials from the space of multiplicators Page 1
Mathematical Notes, Vol. 66, No. 5, 1999 Schr/hdinger Operators with Singular Potentials from …

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 …

We prove that the solution of the Hudson-Parthasarathy quantum stochastic differential
equation in the Fock space coincides with the solution of a symmetric boundary value …

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 …

We show a new remarkable connection between the symmetric form of a quantum stochastic
differential equation (QSDE) and the strong resolvent limit of the Schrödinger equations in …

We discuss the Schrödinger operator with positive singular perturbations given by operators
which act in the space constructed by a positive measure supported by a null set. We …