{
  "id": "1602.08928",
  "version": "v1",
  "published": "2016-02-29T12:07:17.000Z",
  "updated": "2016-02-29T12:07:17.000Z",
  "title": "Aperiodic order and spherical diffraction",
  "authors": [
    "Michael Björklund",
    "Tobias Hartnick",
    "Felix Pogorzelski"
  ],
  "comment": "49 pages, 0 figures, comments are welcome!",
  "categories": [
    "math.DS",
    "math.GR",
    "math.RT"
  ],
  "abstract": "We introduce model sets in arbitrary locally compact second countable (lcsc) groups, generalizing Meyer's definition of a model set in a locally compact abelian group. We then provide a new formulation of diffraction theory, which unlike the classical formulation does not involve F{\\o}lner sets and thus generalizes to point sets in non-amenable lcsc groups. We focus on the case of lcsc groups admitting a Gelfand pair and on the spherical part of the diffraction. Using this approach we obtain explicit formulas for the auto-correlation and diffraction of model sets. Our diffraction formula generalizes the spherical trace formula in a similar way as the abelian diffraction formula generalizes the Poisson summation formula. We deduce that a model set has pure point spherical diffraction provided the underlying lattice is cocompact.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-02-29T12:07:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "model set",
      "aperiodic order",
      "locally compact second countable",
      "lcsc groups",
      "abelian diffraction formula generalizes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 49,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160208928B"
    }
  }
}