{
  "id": "1403.3783",
  "version": "v2",
  "published": "2014-03-15T10:28:06.000Z",
  "updated": "2014-10-15T15:16:13.000Z",
  "title": "Some Positivstellensätze for polynomial matrices",
  "authors": [
    "Lê Công-Trình"
  ],
  "comment": "14 pages, Section 5 rewritten, three references added, final version, to be published in Positivity",
  "doi": "10.1007/s11117-014-0312-6",
  "categories": [
    "math.AG"
  ],
  "abstract": "In this paper we give a version of Krivine-Stengle's Positivstellensatz, Schweighofer's Positivstellensatz, Scheiderer's local-global principle, Scheiderer's Hessian criterion and Marshall's boundary Hessian conditions for polynomial matrices, i.e. matrices with entries from the ring of polynomials in the variables (x_1,...,x_d) with real coefficients. Moreover, we characterize Archimedean quadratic modules of polynomial matrices, and study the relationship between the compactness of a subset in (\\r^{d}) with respect to a subset (\\hoa{G}) of polynomial matrices and the Archimedean property of the preordering and the quadratic module generated by (\\hoa{G}).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-03-15T10:28:06.000Z",
      "abstract": "In this paper we give a version of Krivine-Stengle's Positivstellensatz, Schweighofer's Positivstellensatz, Scheiderer's local-global principle, Scheiderer's Hessian criterion and Marshall's boundary Hessian conditions for polynomial matrices, i.e. matrices with entries from the ring of polynomials in the variables \\(x_1,\\cdots,x_d\\) with real coefficients. Moreover, we characterize Archimedean quadratic modules of polynomial matrices, and study the relationship between the compactness of a subset in \\(\\r^{d}\\) with respect to a subset \\(\\hoa{G}\\) of polynomial matrices and the Archimedean property of the preordering and the quadratic module generated by \\(\\hoa{G}\\).",
      "comment": "14 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-10-15T15:16:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14P99",
      "13J30",
      "15B33",
      "15B48"
    ],
    "keywords": [
      "polynomial matrices",
      "positivstellensätze",
      "marshalls boundary hessian conditions",
      "characterize archimedean quadratic modules",
      "scheiderers local-global principle"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1403.3783C"
    }
  }
}