{
  "id": "2001.02676",
  "version": "v1",
  "published": "2020-01-08T16:03:49.000Z",
  "updated": "2020-01-08T16:03:49.000Z",
  "title": "On the existence of Hurwitz polynomials with no Hadamard factorization",
  "authors": [
    "Stanisław Białas",
    "Michał Góra"
  ],
  "comment": "6 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "A Hurwitz stable polynomial of degree $n\\geq1$ has a Hadamard factorization if it is a Hadamard product (i.e. element-wise multiplication) of two Hurwitz stable polynomials of degree $n$. It is known that Hurwitz stable polynomials of degrees less than four have a Hadamard factorization. We show that for arbitrary $n\\geq4$ there exists a Hurwitz stable polynomial of degree $n$ which does not have a Hadamard factorization.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-08T16:03:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26C10",
      "30C15",
      "93D99"
    ],
    "keywords": [
      "hadamard factorization",
      "hurwitz stable polynomial",
      "hurwitz polynomials",
      "hadamard product"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}