{
  "id": "2501.17712",
  "version": "v1",
  "published": "2025-01-29T15:29:23.000Z",
  "updated": "2025-01-29T15:29:23.000Z",
  "title": "Constructing self-similar subsets within the fractal support of LWS for their multifractal analysis",
  "authors": [
    "Céline Esser",
    "Béatrice Vedel"
  ],
  "categories": [
    "math.CA",
    "math.MG",
    "math.PR"
  ],
  "abstract": "Given a fractal $\\mathcal{I}$ whose Hausdorff dimension matches with the upper-box dimension, we propose a new method which consists in selecting inside $\\mathcal{I}$ some subsets (called quasi-Cantor sets) of almost same dimension and with controled properties of self-similarties at prescribed scales. It allows us to estimate below the Hausdorff dimension $\\mathcal{I}$ intersected to limsup sets of contracted balls selected according a Bernoulli law, in contexts where classical Mass Transference Principles cannot be applied. We apply this result to the computation of the increasing multifractal spectrum of lacunary wavelet series supported on $\\mathcal{I}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-01-29T15:29:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42C40",
      "28A78",
      "28A80",
      "26A16",
      "60G17"
    ],
    "keywords": [
      "constructing self-similar subsets",
      "multifractal analysis",
      "fractal support",
      "hausdorff dimension matches",
      "lacunary wavelet series"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}