{
  "id": "1301.4747",
  "version": "v2",
  "published": "2013-01-21T04:01:42.000Z",
  "updated": "2013-10-17T14:39:44.000Z",
  "title": "Hausdorff dimension of level sets of generalized Takagi functions",
  "authors": [
    "Pieter C. Allaart"
  ],
  "comment": "34 pages, 5 figures. The statement of Theorem 1.1 was expanded and various improvements to the presentation were made",
  "doi": "10.1017/S0305004114000309",
  "categories": [
    "math.CA"
  ],
  "abstract": "This paper examines level sets of two families of continuous, nowhere differentiable functions (one a subfamily of the other) defined in terms of the \"tent map\". The well-known Takagi function is a special case. Sharp upper bounds are given for the Hausdorff dimension of the level sets of functions in these two families. Furthermore, the case where a function f is chosen at random from either family is considered, and results are given for the Hausdorff dimension of the zero set and the set of maximum points of f.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-10-17T14:39:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26A27",
      "28A78"
    ],
    "keywords": [
      "hausdorff dimension",
      "generalized takagi functions",
      "paper examines level sets",
      "sharp upper bounds",
      "well-known takagi function"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Mathematical Proceedings of the Cambridge Philosophical Society",
      "year": 2014,
      "month": "Sep",
      "volume": 157,
      "number": 2,
      "pages": 253
    },
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014MPCPS.157..253A"
    }
  }
}