Radial positive definite functions and spectral theory of the Schrödinger operators with point interactions
We complete the classical Schoenberg representation theorem for radial positive definite functions. We apply this result to study spectral properties of self-adjoint realizations of two- and three-dimensional Schrödinger operators with point interactions on a finite set. In particular, we prove that any realization has purely absolutely continuous non-negative spectrum.
math.SP↗