{
  "id": "1409.0699",
  "version": "v1",
  "published": "2014-09-02T13:36:30.000Z",
  "updated": "2014-09-02T13:36:30.000Z",
  "title": "Symmetric semi-algebraic sets and non-negativity of symmetric polynomials",
  "authors": [
    "Cordian Riener"
  ],
  "comment": "6 pages",
  "categories": [
    "math.OC"
  ],
  "abstract": "The question of how to certify the non-negativity of a polynomial function lies at the heart of Real Algebra and it also has important applications to Optimization. In the setting of symmetric polynomials Timofte provided a useful way of certifying non-negativity of symmetric polynomials that are of a fixed degree. In this note we present more general results which naturally generalize Timofte's setting. We investigate families of polynomials that allow special representations in terms of power-sum polynomials.These in particular also include the case of symmetric polynomials of fixed degree. Therefore, we recover the consequences of Timofte's original statements as a corollary. Thus, this note also provides an alternative and simple proof of Timofte's original statements.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-09-02T13:36:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "symmetric semi-algebraic sets",
      "non-negativity",
      "timoftes original statements",
      "fixed degree",
      "polynomial function lies"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1409.0699R"
    }
  }
}