{
  "id": "2104.03955",
  "version": "v1",
  "published": "2021-04-08T17:56:35.000Z",
  "updated": "2021-04-08T17:56:35.000Z",
  "title": "On the Rajchman property for self-similar measures on $\\mathbb{R}^{d}$",
  "authors": [
    "Ariel Rapaport"
  ],
  "comment": "41 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "We establish a complete algebraic characterization of self-similar iterated function systems $\\Phi$ on $\\mathbb{R}^{d}$, for which there exists a positive probability vector $p$ so that the Fourier transform of the self-similar measure corresponding to $\\Phi$ and $p$ does not tend to $0$ at infinity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-04-08T17:56:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "28A80",
      "42A16"
    ],
    "keywords": [
      "self-similar measure",
      "rajchman property",
      "complete algebraic characterization",
      "self-similar iterated function systems",
      "fourier transform"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 41,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}