{
  "id": "math/9811144",
  "version": "v1",
  "published": "1998-11-24T18:20:53.000Z",
  "updated": "1998-11-24T18:20:53.000Z",
  "title": "Frames of translates",
  "authors": [
    "Peter G. Casazza",
    "Ole Christensen",
    "Nigel J. Kalton"
  ],
  "comment": "23 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "We give necessary and sufficient conditions for a subfamily of regularly spaced translates of a function to form a frame (resp. a Riesz basis) for its span. One consequence is that ifthetranslates are taken only from a subset of the natural numbers, then this family is a frame if and only if it is a Riesz basis. We also consider arbitrary sequences of translates and show that for sparse sets, having an upper frame bound is equivalent to the family being a frame sequence. Finally, we use the fractional Hausdorff dimension to identify classes of exact frame sequences.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1998-11-24T18:20:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46C05",
      "46B20"
    ],
    "keywords": [
      "translates",
      "riesz basis",
      "exact frame sequences",
      "upper frame bound",
      "fractional hausdorff dimension"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1998math.....11144C"
    }
  }
}