{
  "id": "math/0504071",
  "version": "v1",
  "published": "2005-04-05T12:44:15.000Z",
  "updated": "2005-04-05T12:44:15.000Z",
  "title": "Reproducing kernel Hilbert spaces and Mercer theorem",
  "authors": [
    "Claudio Carmeli",
    "Ernesto De Vito",
    "Alessandro Toigo"
  ],
  "comment": "30 pages, Latex2e",
  "categories": [
    "math.FA",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We characterize the reproducing kernel Hilbert spaces whose elements are $p$-integrable functions in terms of the boundedness of the integral operator whose kernel is the reproducing kernel. Moreover, for $p=2$ we show that the spectral decomposition of this integral operator gives a complete description of the reproducing kernel.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-04-05T12:44:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "reproducing kernel hilbert spaces",
      "mercer theorem",
      "integral operator",
      "spectral decomposition",
      "complete description"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......4071C"
    }
  }
}