{
  "id": "1512.02049",
  "version": "v1",
  "published": "2015-12-07T14:07:10.000Z",
  "updated": "2015-12-07T14:07:10.000Z",
  "title": "Polynomial approximation of self-similar measures and the spectrum of the transfer operator",
  "authors": [
    "Christoph Bandt",
    "Helena Peña"
  ],
  "comment": "14 pages, 7 figures",
  "categories": [
    "math.DS"
  ],
  "abstract": "We consider self-similar measures on $\\mathbb R.$ The Hutchinson operator $H$ acts on measures and is the dual of the transfer operator $T$ which acts on continuous functions. We determine polynomial eigenfunctions of $T .$ As a consequence, we obtain eigenvalues of $H$ and natural polynomial approximations of the self-similar measure. Bernoulli convolutions are studied as an example.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-12-07T14:07:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "28A80",
      "37C30"
    ],
    "keywords": [
      "self-similar measure",
      "transfer operator",
      "natural polynomial approximations",
      "determine polynomial eigenfunctions",
      "bernoulli convolutions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}