{
  "id": "1610.07658",
  "version": "v1",
  "published": "2016-10-24T21:38:03.000Z",
  "updated": "2016-10-24T21:38:03.000Z",
  "title": "On transfer operators on the circle with trigonometric weights",
  "authors": [
    "Xianghong Chen",
    "Hans Volkmer"
  ],
  "comment": "30 pages, 4 figures",
  "categories": [
    "math.DS",
    "math.CA",
    "math.NT"
  ],
  "abstract": "We study spectral properties of the transfer operators $L$ defined on the circle $\\mathbb T=\\mathbb R/\\mathbb Z$ by $$(Lu)(t)=\\frac{1}{d}\\sum_{i=0}^{d-1} f\\left(\\frac{t+i}{d}\\right)u\\left(\\frac{t+i}{d}\\right),\\ t\\in\\mathbb T$$ where $u$ is a function on $\\mathbb T$. We focus in particular on the cases $f(t)=|\\cos(\\pi t)|^q$ and $f(t)=|\\sin(\\pi t)|^q$, which are closely related to some classical Fourier-analytic questions. We also obtain some explicit computations, particularly in the case $d=2$. Our study extends work of Strichartz \\cite{Strichartz1990} and Fan and Lau \\cite{FanLau1998}.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-10-24T21:38:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37C30",
      "37E10",
      "35P15",
      "37N99"
    ],
    "keywords": [
      "transfer operators",
      "trigonometric weights",
      "study spectral properties",
      "study extends work",
      "classical fourier-analytic questions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}