{
  "id": "1002.0672",
  "version": "v2",
  "published": "2010-02-03T09:20:52.000Z",
  "updated": "2010-12-16T16:02:39.000Z",
  "title": "The Gelfand widths of $\\ell_p$-balls for $0<p\\leq 1$",
  "authors": [
    "Simon Foucart",
    "Alain Pajor",
    "Holger Rauhut",
    "Tino Ullrich"
  ],
  "comment": "15 pages",
  "journal": "Journal of Complexity 26 (2010) 629-640",
  "doi": "10.1016/j.jco.2010.04.004",
  "categories": [
    "math.FA",
    "cs.IT",
    "math.IT"
  ],
  "abstract": "We provide sharp lower and upper bounds for the Gelfand widths of $\\ell_p$-balls in the $N$-dimensional $\\ell_q^N$-space for $0<p\\leq 1$ and $p<q \\leq 2$. Such estimates are highly relevant to the novel theory of compressive sensing, and our proofs rely on methods from this area.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-12-16T16:02:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "41A46",
      "46B09"
    ],
    "keywords": [
      "gelfand widths",
      "sharp lower",
      "upper bounds",
      "novel theory",
      "highly relevant"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1002.0672F"
    }
  }
}