{
  "id": "1912.12478",
  "version": "v1",
  "published": "2019-12-28T16:06:37.000Z",
  "updated": "2019-12-28T16:06:37.000Z",
  "title": "Extra-invariance of group actions",
  "authors": [
    "C. Cabrelli",
    "C. A. Mosquera",
    "V. Paternostro"
  ],
  "comment": "16 pages, 2 figures",
  "categories": [
    "math.FA"
  ],
  "abstract": "Given discrete groups $\\Gamma \\subset \\Delta$ we characterize $(\\Gamma,\\sigma)$-invariant spaces that are also invariant under $\\Delta$. This will be done in terms of subspaces that we define using an appropriate Zak transform and a particular partition of the underlying group. On the way, we obtain a new characterization of principal $(\\Gamma,\\sigma)$-invariant spaces in terms of the Zak transform of its generator. This result is in the spirit of the analogous in the context of shift-invariant spaces in terms of the Fourier transform, which is very well-known. As a consequence of our results, we give a solution for the problem of finding the $(\\Gamma,\\sigma)$-invariant space nearest - in the sense of least squares - to a given set of data.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-28T16:06:37.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "group actions",
      "extra-invariance",
      "appropriate zak transform",
      "invariant space nearest",
      "shift-invariant spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}