{
  "id": "1007.2002",
  "version": "v2",
  "published": "2010-07-12T22:31:33.000Z",
  "updated": "2011-09-02T18:43:44.000Z",
  "title": "On the finite linear independence of lattice Gabor systems",
  "authors": [
    "Ciprian Demeter",
    "S. Zubin Gautam"
  ],
  "comment": "13 pages, no figures. Minor errors corrected, additional explanation added to proofs in Section 4",
  "categories": [
    "math.CA",
    "math.FA"
  ],
  "abstract": "In the restricted setting of product phase space lattices, we give an alternate proof of P. Linnell's theorem on the finite linear independence of lattice Gabor systems in $L^2(\\mathbb R^d)$. Our proof is based on a simple argument from the spectral theory of random Schr\\\"odinger operators; in the one-dimensional setting, we recover the full strength of Linnell's result for general lattices.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-09-02T18:43:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42C40",
      "42B99",
      "26B99",
      "46B15"
    ],
    "keywords": [
      "lattice gabor systems",
      "finite linear independence",
      "product phase space lattices",
      "linnells result",
      "full strength"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1007.2002D"
    }
  }
}