Rank one perturbations, approximations, and selfadjoint extensions (Q1365230)

Let \(A\) be a selfadjoint positive operator in a Hilbert space \({\mathcal H}\). Let \({\mathcal H}_p(A)\), \(p\in\mathbb{Z}\) be the standard scale of Banach spaces associated to \(A\). There are considered selfadjoint realizations of rank one perturbations \(A_\alpha= A+\alpha(\varphi,.)\varphi\) for \(\varphi\in{\mathcal H}_{-2}(A)\) and for a finite or infinite coupling constant \(\alpha\). The abstract theory is applied to Schrödinger operators in \(L^2(\mathbb{R}^3)\) with delta like potentials.