{
  "id": "1801.10026",
  "version": "v1",
  "published": "2018-01-27T16:35:41.000Z",
  "updated": "2018-01-27T16:35:41.000Z",
  "title": "Gabor frames for model sets",
  "authors": [
    "Ewa Matusiak"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:1801.05213",
  "categories": [
    "math.FA",
    "math.OA"
  ],
  "abstract": "We generalize three main concepts of Gabor analysis for lattices to the setting of model sets: Fundamental Identity of Gabor Analysis, Janssen's representation of the frame operator and Wexler-Raz biorthogonality relations. Utilizing the connection between model sets and almost periodic functions, as well as Poisson's summations formula for model sets we develop a form of a bracket product that plays a central role in our approach. Furthermore, we show that, if a Gabor system for a model set admits a dual which is of Gabor type, then the density of the model set has to be greater than one.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-27T16:35:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "gabor frames",
      "gabor analysis",
      "wexler-raz biorthogonality relations",
      "poissons summations formula",
      "model set admits"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}