{
  "id": "2009.01703",
  "version": "v1",
  "published": "2020-09-03T14:31:24.000Z",
  "updated": "2020-09-03T14:31:24.000Z",
  "title": "Fourier transform and expanding maps on Cantor sets",
  "authors": [
    "Tuomas Sahlsten",
    "Connor Stevens"
  ],
  "comment": "This article draws heavily some key arguments from our earlier work arXiv:1810.01378 on infinite branches, which will be revised later for just the Gauss map case",
  "categories": [
    "math.DS",
    "math.CA"
  ],
  "abstract": "We study the Fourier transforms $\\widehat{\\mu}(\\xi)$ of Gibbs measures $\\mu$ for uniformly expanding maps $T$ of bounded distortions on Cantor sets with strong separation condition. When $T$ is totally non-linear and Hausdorff dimension of $\\mu$ is large enough, then $\\widehat{\\mu}(\\xi)$ decays at a polynomial rate as $|\\xi| \\to \\infty$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-09-03T14:31:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fourier transform",
      "cantor sets",
      "expanding maps",
      "strong separation condition",
      "gibbs measures"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}