{
  "id": "1212.4679",
  "version": "v2",
  "published": "2012-12-19T14:44:06.000Z",
  "updated": "2013-11-20T11:14:43.000Z",
  "title": "Multi-tiling and Riesz bases",
  "authors": [
    "Sigrid Grepstad",
    "Nir Lev"
  ],
  "journal": "Advances in Mathematics, Vol. 252, p. 1-6, 2014",
  "categories": [
    "math.CA",
    "math.FA"
  ],
  "abstract": "Let S be a bounded, Riemann measurable set in R^d, and L be a lattice. By a theorem of Fuglede, if S tiles R^d with translation set L, then S has an orthogonal basis of exponentials. We show that, under the more general condition that S multi-tiles R^d with translation set L, S has a Riesz basis of exponentials. The proof is based on Meyer's quasicrystals.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-11-20T11:14:43.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "riesz bases",
      "translation set",
      "riemann measurable set",
      "riesz basis",
      "multi-tiling"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier",
      "journal": "Adv. Math."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1212.4679G"
    }
  }
}