{
  "id": "1811.03586",
  "version": "v1",
  "published": "2018-11-08T18:14:29.000Z",
  "updated": "2018-11-08T18:14:29.000Z",
  "title": "A version of Putinar's Positivstellensatz for cylinders",
  "authors": [
    "Paula Escorcielo",
    "Daniel Perrucci"
  ],
  "categories": [
    "math.AG"
  ],
  "abstract": "We prove that, under some additional assumption, Putinar's Positivstellensatz holds on cylinders of type $S \\times {\\mathbb R}$ with $S = \\{x \\in {\\mathbb R}^n | g_1(x) \\ge 0, ..., g_s(x) \\ge 0\\}$ such that the quadratic module generated by $g_1, ..., g_s$ in ${\\mathbb R}[X_1, ..., X_n]$ is archimedean, and we provide a degree bound for the representation of a polynomial $f \\in {\\mathbb R}[X_1, ..., X_n, Y]$ which is positive on $S \\times {\\mathbb R}$ as an explicit element of the quadratic module generated by $g_1, ..., g_s$ in ${\\mathbb R}[X_1, ..., X_n, Y]$. We also include an example to show that an additional assumption is necessary for Putinar's Positivstellensatz to hold on cylinders of this type.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-08T18:14:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "12D15",
      "13J30",
      "14P10"
    ],
    "keywords": [
      "additional assumption",
      "quadratic module",
      "putinars positivstellensatz holds",
      "explicit element",
      "degree bound"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}