Perturbation of the Laplacian by the Coulomb potential and a point interaction in L p (?)3

Abstract

Perturbations of -Δ+α/|x| (with α>0) by a point interaction centered at zero are defined in Lp(ℝ3). This is done for 3/2<p<3 by extending the operator -Δ+α/|x| restricted to C0∞(ℝ3∖{0}), such that the extension is the negative generator of an analytic semigroup on Lp(ℝ3).