{
  "id": "1211.0337",
  "version": "v1",
  "published": "2012-11-02T01:08:51.000Z",
  "updated": "2012-11-02T01:08:51.000Z",
  "title": "Linear Independence of Finite Gabor Systems Determined by Behavior at Infinity",
  "authors": [
    "John J. Benedetto",
    "Abdelkrim Bourouihiya"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "We prove that the HRT (Heil, Ramanathan, and Topiwala) conjecture holds for finite Gabor systems generated by square-integrable functions with certain behavior at infinity. These functions include functions ultimately decaying faster than any exponential function, as well as square-integrable functions ultimately analytic and whose germs are in a Hardy field. Two classes of the latter type of functions are the set of square-integrable logarithmico-exponential functions and the set of square-integrable Pfaffian functions. We also prove the HRT conjecture for certain finite Gabor systems generated by positive functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-11-02T01:08:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "linear independence",
      "square-integrable functions",
      "square-integrable pfaffian functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1211.0337B"
    }
  }
}