{
  "id": "math/0611946",
  "version": "v1",
  "published": "2006-11-30T12:28:04.000Z",
  "updated": "2006-11-30T12:28:04.000Z",
  "title": "Linear polarization constant of $\\R^n$",
  "authors": [
    "Mate Matolcsi"
  ],
  "comment": "8 pages",
  "journal": "Acta Math. Hungar. 108 (2005), no. 1-2, 129--136",
  "categories": [
    "math.CA"
  ],
  "abstract": "The present work contributes to the determination of the $n$-th linear polarization constant $c_n(H)$ of an $n$-dimensional real Hilbert space $H$. We provide some new lower bounds on the value of $\\sup_{\\|y\\|=1}| x_1,y >... x_n,y |$, where $x_1, ..., x_n$ are unit vectors in $H$. In particular, the results improve an earlier estimate of Marcus. However, the intriguing conjecture $c_n(H)=n^{n/2}$ remains open.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-11-30T12:28:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46G25",
      "52A40",
      "46B07"
    ],
    "keywords": [
      "dimensional real hilbert space",
      "th linear polarization constant",
      "work contributes",
      "lower bounds",
      "unit vectors"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....11946M"
    }
  }
}