{
  "id": "math/0703379",
  "version": "v1",
  "published": "2007-03-13T15:14:07.000Z",
  "updated": "2007-03-13T15:14:07.000Z",
  "title": "Gabor frames without inequalities",
  "authors": [
    "Karlheinz Gröchenig"
  ],
  "comment": "16 pages",
  "journal": "International Mathematics Research Notices 2007 (2007), rnm111-21",
  "categories": [
    "math.FA",
    "math.OA"
  ],
  "abstract": "We prove fourteen equivalent conditions for a set of timefrequency shifts on a lattice to be a frame for L^2. Remarkably, several of these conditions can be formulated without an inequality. In particular, instead of checking the invertibility of the frame operator on L^2 it suffices to verify that it is one-to-one on a certain subspace of tempered distributions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-03-13T15:14:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42C15",
      "22E25"
    ],
    "keywords": [
      "gabor frames",
      "inequality",
      "fourteen equivalent conditions",
      "timefrequency shifts",
      "frame operator"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......3379G"
    }
  }
}