{
  "id": "1107.3874",
  "version": "v2",
  "published": "2011-07-20T02:09:12.000Z",
  "updated": "2011-10-16T06:28:42.000Z",
  "title": "Fourier and Cauchy-Stieltjes transforms of power laws including stable distributions",
  "authors": [
    "Takahiro Hasebe"
  ],
  "comment": "18 pages, Subsection 2.5 withdrawn, accepted for publication in Internat. J. Math",
  "journal": "Internat. J. Math. 23, No. 3 (2012), 1250041 (21 pages)",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP",
    "math.OA"
  ],
  "abstract": "We introduce a class of probability measures whose densities near infinity are mixtures of Pareto distributions. This class can be characterized by the Fourier transform which has a power series expansion including real powers, not only integer powers. This class includes stable distributions in probability and also non-commutative probability theories. We also characterize the class in terms of the Cauchy-Stieltjes transform and the Voiculescu transform. If the stability index is greater than one, stable distributions in probability theory do not belong to that class, while they do in non-commutative probability.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-10-16T06:28:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60E07",
      "30B10",
      "46L53",
      "46L54"
    ],
    "keywords": [
      "stable distributions",
      "cauchy-stieltjes transform",
      "power laws",
      "probability theory",
      "power series expansion"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1107.3874H"
    }
  }
}