{
  "id": "1807.07011",
  "version": "v1",
  "published": "2018-07-18T16:00:56.000Z",
  "updated": "2018-07-18T16:00:56.000Z",
  "title": "Time-frequency analysis on the adeles over the rationals",
  "authors": [
    "Ulrik B. R. Enstad",
    "Mads S. Jakobsen",
    "Franz Luef"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "We show that the construction of Gabor frames in $L^{2}(\\mathbb{R})$ with generators in $\\mathbf{S}_{0}(\\mathbb{R})$ and with respect to time-frequency shifts from a rectangular lattice $\\alpha\\mathbb{Z}\\times\\beta\\mathbb{Z}$ is equivalent to the construction of certain Gabor frames for $L^{2}$ over the adeles over the rationals and the group $\\mathbb{R}\\times\\mathbb{Q}_{p}$. Furthermore, we detail the connection between the construction of Gabor frames on the adeles and on $\\mathbb{R}\\times\\mathbb{Q}_{p}$ with the construction of certain Heisenberg modules.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-07-18T16:00:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "time-frequency analysis",
      "gabor frames",
      "construction",
      "heisenberg modules",
      "rectangular lattice"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}