{
  "id": "1208.1203",
  "version": "v1",
  "published": "2012-08-06T16:29:47.000Z",
  "updated": "2012-08-06T16:29:47.000Z",
  "title": "Spectral theory of Schrödinger operators with infinitely many point interactions and radial positive definite functions",
  "authors": [
    "Mark M. Malamud",
    "Konrad Schmüdgen"
  ],
  "comment": "to appear in Journal of Functional Analysis",
  "categories": [
    "math.FA"
  ],
  "abstract": "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-08-06T16:29:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A10",
      "47B25"
    ],
    "keywords": [
      "radial positive definite functions",
      "point interactions",
      "spectral theory",
      "schrödinger operators",
      "absolutely continuous non-negative spectrum"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1208.1203M"
    }
  }
}