{
  "id": "2201.01909",
  "version": "v2",
  "published": "2022-01-06T03:43:34.000Z",
  "updated": "2022-04-02T07:48:14.000Z",
  "title": "Matrix representations for some self-similar measures on $\\mathbb{R}^{d}$",
  "authors": [
    "Yu-Feng Wu"
  ],
  "comment": "Accepted for publication in Mathematische Zeitschrift",
  "categories": [
    "math.CA"
  ],
  "abstract": "We establish matrix representations for self-similar measures on $\\mathbb{R}^d$ generated by equicontractive IFSs satisfying the finite type condition. As an application, we prove that the $L^q$-spectrum of every such self-similar measure is differentiable on $(0,\\infty)$. This extends an earlier result of Feng (J. Lond. Math. Soc.(2) 68(1):102--118, 2003) to higher dimensions.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2022-04-02T07:48:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "28A80"
    ],
    "keywords": [
      "self-similar measure",
      "finite type condition",
      "higher dimensions",
      "establish matrix representations",
      "earlier result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}