{
  "id": "1505.05867",
  "version": "v1",
  "published": "2015-05-21T19:57:39.000Z",
  "updated": "2015-05-21T19:57:39.000Z",
  "title": "Volumes of unit balls of mixed sequence spaces",
  "authors": [
    "Henning Kempka",
    "Jan Vybíral"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "The volume of the unit ball of the Lebesgue sequence space $\\ell_p^m$ is very well known since the times of Dirichlet. We calculate the volume of the unit ball in the mixed norm $\\ell^n_q(\\ell_p^m)$, whose special cases are nowadays popular in machine learning under the name of group lasso. We consider the real as well as the complex case. The result is given by a closed formula involving the gamma function, only slightly more complicated than the one of Dirichlet. We close by an overview of open problems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-05-21T19:57:39.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "unit ball",
      "mixed sequence spaces",
      "lebesgue sequence space",
      "open problems",
      "gamma function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150505867K"
    }
  }
}