{
  "id": "0905.1426",
  "version": "v2",
  "published": "2009-05-09T18:39:00.000Z",
  "updated": "2011-01-09T00:41:35.000Z",
  "title": "Polarization of an inequality",
  "authors": [
    "Ivo Klemes"
  ],
  "comment": "9 pages. Updated references and remarks in section 3. Accepted in Math. Inequalities and Appl",
  "categories": [
    "math.CA",
    "math.SP"
  ],
  "abstract": "We generalize a previous inequality related to a sharp version of the Littlewood conjecture on the minimal $L_1$-norm of $N$-term exponential sums $f$ on the unit circle. The new result concerns replacing the expression $\\log(1+t|f|^2)$ with $\\log (\\sum_{k=1}^K t_k|f_{k}|^2)$. The proof occurs on the level of finite Toeplitz matrices, where it reduces to an inequality between their polarized determinants (or \"mixed discriminants\").",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-01-09T00:41:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42A32",
      "15A42",
      "15A15"
    ],
    "keywords": [
      "inequality",
      "polarization",
      "term exponential sums",
      "finite toeplitz matrices",
      "sharp version"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0905.1426K"
    }
  }
}