{
  "id": "math/0201161",
  "version": "v1",
  "published": "2002-01-17T13:45:06.000Z",
  "updated": "2002-01-17T13:45:06.000Z",
  "title": "Compactness Criteria in Function Spaces",
  "authors": [
    "Monika Dörfler",
    "Hans G. Feichtinger",
    "Karlheinz Gröchenig"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "The classical criterion for compactness in Banach spaces of functions can be reformulated into a simple tightness condition in the time-frequency domain. This description preserves more explicitly the symmetry between time and frequency than the classical conditions. The result is first stated and proved for L^2(R^d), and then generalized to coorbit spaces. As special cases, we obtain new characterizations of compactness in Besov-Triebel-Lizorkin spaces, modulation spaces and Bargmann-Fock spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-01-17T13:45:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B50",
      "42B35"
    ],
    "keywords": [
      "function spaces",
      "compactness criteria",
      "simple tightness condition",
      "besov-triebel-lizorkin spaces",
      "banach spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......1161D"
    }
  }
}