Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4590685 | Journal of Functional Analysis | 2012 | 51 Pages |
Abstract
A number of results on radial positive definite functions on Rn related to Schoenbergʼs integral representation theorem are obtained. They are applied to the study of spectral properties of self-adjoint realizations of two- and three-dimensional Schrödinger 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 Schrödinger operators to obtain new results on completely monotone functions.
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