{
  "id": "1011.6602",
  "version": "v2",
  "published": "2010-11-30T16:38:05.000Z",
  "updated": "2010-12-15T18:29:59.000Z",
  "title": "Construction of Multivariate Gaussian Weyl--Heisenberg Frames, (I)",
  "authors": [
    "Maurice de Gosson"
  ],
  "comment": "Corrected version of a withdrawn submission; This Note replaces a former note which contains an incorrect proof",
  "categories": [
    "math-ph",
    "math.FA",
    "math.MP",
    "math.SG",
    "quant-ph"
  ],
  "abstract": "Let {\\phi} be an arbitrary generalized Gaussian (squeezed coherent state), {\\Lambda}_{{\\alpha}{\\beta}}=({\\alpha}_1 Z \\times\\cdot\\cdot\\cdot\\times \\alpha_{n}\\mathbb{Z)\\times}(\\beta_{1}\\mathbb{Z}\\times\\cdot\\cdot\\cdot \\times\\beta_{n}\\mathbb{Z)}$ a rectangular lattice. We show that there exists a positive definite symplectic matrix M (depending on {\\phi}) such that the multivariate Weyl--Heisenberg system G({\\phi},M{\\Lambda}_{{\\alpha}{\\beta}}) is a frame. In a forthcoming Note we will prove a converse to this result.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-12-15T18:29:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "multivariate gaussian weyl-heisenberg frames",
      "construction",
      "multivariate weyl-heisenberg system",
      "positive definite symplectic matrix",
      "squeezed coherent state"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1011.6602D"
    }
  }
}