{
  "id": "0705.0318",
  "version": "v1",
  "published": "2007-05-02T16:02:10.000Z",
  "updated": "2007-05-02T16:02:10.000Z",
  "title": "Decomposition of spaces of distributions induced by Hermite expansions",
  "authors": [
    "Pencho Petrushev",
    "Yuan Xu"
  ],
  "comment": "34 pages",
  "categories": [
    "math.CA",
    "math.FA"
  ],
  "abstract": "Decomposition systems with rapidly decaying elements (needlets) based on Hermite functions are introduced and explored. It is proved that the Triebel-Lizorkin and Besov spaces on $\\R^d$ induced by Hermite expansions can be characterized in terms of the needlet coefficients. It is also shown that the Hermite Triebel-Lizorkin and Besov spaces are, in general, different from the respective classical spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-05-02T16:02:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B35",
      "42C15"
    ],
    "keywords": [
      "hermite expansions",
      "distributions",
      "besov spaces",
      "hermite triebel-lizorkin",
      "needlet coefficients"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0705.0318P"
    }
  }
}