Mark M. Malamud, Konrad Schmüdgen
Published 2012-08-06Version 1
A number of results on radial positive definite functions on ${\mathbb R^n}$ related to Schoenberg's integral representation theorem are obtained. They are applied to the study of spectral properties of self-adjoint realizations of two- and three-dimensional Schr\"odinger operators with countably many point interactions. In particular, we find conditions on the configuration of point interactions such that any self-adjoint realization has purely absolutely continuous non-negative spectrum. We also apply some results on Schr\"odinger operators to obtain new results on completely monotone functions.
Comments: to appear in Journal of Functional Analysis
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