{
  "id": "1503.02160",
  "version": "v1",
  "published": "2015-03-07T11:04:06.000Z",
  "updated": "2015-03-07T11:04:06.000Z",
  "title": "On Gabor frames generated by sign-changing windows and B-splines",
  "authors": [
    "Ole Christensen",
    "Hong Oh Kim",
    "Rae Young Kim"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "For a class of compactly supported windows we characterize the frame property for a Gabor system $\\mts,$ for translation parameters $a$ belonging to a certain range depending on the support size. We show that the obstructions to the frame property are located on a countable number of \"curves.\" For functions that are positive on the interior of the support these obstructions do not appear, and the considered region in the $(a,b)$ plane is fully contained in the frame set. In particular this confirms a recent conjecture about B-splines by Gr\\\"ochenig in that particular region. We prove that the full conjecture is true if it can be proved in a certain \"hyperbolic strip.\"",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-03-07T11:04:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42C15"
    ],
    "keywords": [
      "gabor frames",
      "sign-changing windows",
      "frame property",
      "gabor system",
      "translation parameters"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}