{
  "id": "1212.1553",
  "version": "v2",
  "published": "2012-12-07T08:14:09.000Z",
  "updated": "2013-04-01T16:40:48.000Z",
  "title": "On the Fourier transforms of self-similar measures",
  "authors": [
    "Masato Tsujii"
  ],
  "comment": "16 pages, 1 figure Several errors in the previous version are corrected. A few notations are changed for clearer exposition",
  "categories": [
    "math.DS"
  ],
  "abstract": "For the Fourier transform $\\mathcal{F}\\mu$ of a general (non-trivial) self-similar measure $\\mu$ on the real line $\\mathbb{R}$, we prove a large deviation estimate \\[ \\lim_{c\\to +0} \\varlimsup_{t\\to \\infty}\\frac{1}{t}\\log (\\mathrm{Leb}\\{x\\in [-e^t, e^t]\\mid |\\mathcal{F}\\mu(\\xi)| \\ge e^{-ct} \\})=0. \\]",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-04-01T16:40:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "28A80",
      "42A38"
    ],
    "keywords": [
      "fourier transform",
      "self-similar measure",
      "large deviation estimate",
      "real line"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1212.1553T"
    }
  }
}