Schrödinger operators with point interactions and radial positive definite functions (Q352222)

The authors consider Schrödinger operators with point interactions. In dimension larger than one, the extension of this operator on Sobolev functions of class \(W^{1,2}\) is problematic due to the lack of continuity. In dimension 3, Berezin and Faddeev proposed an extension to \(W^{2,2}\) functions which vanish at these points. In this paper, self-adjointness, lower semi-boundedness and finiteness of the negative spectrum are proved for possibly infinitely-many singularities with mutual distance bounded from below.