{
  "id": "math/0312321",
  "version": "v5",
  "published": "2003-12-17T12:25:19.000Z",
  "updated": "2007-10-20T11:03:14.000Z",
  "title": "Convexity properties of twisted root maps",
  "authors": [
    "Julius Borcea"
  ],
  "comment": "final version, to appear in Rocky Mountain J. Math.; 14 pages, no figures, LaTeX2e",
  "journal": "Rocky Mountain J. Math. 38 (2008), 809-834",
  "categories": [
    "math.CA",
    "math.CV"
  ],
  "abstract": "The strong spectral order induces a natural partial ordering on the manifold $H_{n}$ of monic hyperbolic polynomials of degree $n$. We prove that twisted root maps associated with linear operators acting on $H_{n}$ are G\\aa rding convex on every polynomial pencil and we characterize the class of polynomial pencils of logarithmic derivative type by means of the strong spectral order. Let $A'$ be the monoid of linear operators that preserve hyperbolicity as well as root sums. We show that any polynomial in $H_{n}$ is the global minimum of its $A'$-orbit and we conjecture a similar result for complex polynomials.",
  "revisions": [
    {
      "version": "v5",
      "updated": "2007-10-20T11:03:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "39B62",
      "26C10",
      "30C15",
      "60E15"
    ],
    "keywords": [
      "twisted root maps",
      "convexity properties",
      "strong spectral order induces",
      "polynomial pencil",
      "linear operators"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math.....12321B"
    }
  }
}