{
  "id": "1706.07184",
  "version": "v1",
  "published": "2017-06-22T07:13:58.000Z",
  "updated": "2017-06-22T07:13:58.000Z",
  "title": "Decrease of Fourier coefficients of stationary measures",
  "authors": [
    "Jialun Li"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "Let $\\mu$ be a Borel probability measure on $\\mathrm{SL}_2(\\mathbb R)$ with a finite exponential moment, and assume that the subgroup $\\Gamma_{\\mu}$ generated by the support of $\\mu$ is Zariski dense. Let $\\nu$ be the unique $\\mu-$stationary measure on $\\mathbb P^1_{\\mathbb R}$. We prove that the Fourier coefficients $\\widehat{\\nu}(k)$ of $\\nu$ converge to $0$ as $|k|$ tends to infinity. Our proof relies on a generalized renewal theorem for the Cartan projection.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-06-22T07:13:58.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "stationary measure",
      "fourier coefficients",
      "borel probability measure",
      "finite exponential moment",
      "zariski dense"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}