{
  "id": "1412.2650",
  "version": "v1",
  "published": "2014-12-08T16:20:29.000Z",
  "updated": "2014-12-08T16:20:29.000Z",
  "title": "Equivalence of modes of convergence on reproducing kernel Hilbert spaces",
  "authors": [
    "D. Azevedo"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "Let $(X,\\mu)$ be a strictly-positive Borel measure space. We show that the modes of convergence in a reproducing kernel Hilbert (RKHS) space, pointwise, weak, strong are all equivalents. From this we describe some important consequences such as an association with positive operators and positive definite kernels and a compact embedding condition for a RKHS in $L^{2}(X,\\mu)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-12-08T16:20:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46E22",
      "40A30",
      "47B32",
      "47B65",
      "57R40"
    ],
    "keywords": [
      "reproducing kernel hilbert spaces",
      "convergence",
      "equivalence",
      "strictly-positive borel measure space",
      "compact embedding condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1412.2650A"
    }
  }
}