{
  "id": "1302.4506",
  "version": "v1",
  "published": "2013-02-19T02:32:39.000Z",
  "updated": "2013-02-19T02:32:39.000Z",
  "title": "More symmetric polynomials related to p-norms",
  "authors": [
    "Ivo Klemes"
  ],
  "comment": "27 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "It is known that the elementary symmetric polynomials $e_k(x)$ have the property that if $ x, y \\in [0,\\infty)^n$ and $e_k(x) \\leq e_k(y)$ for all $k$, then $||x||_p \\leq ||y||_p$ for all real $0\\leq p \\leq 1$, and moreover $||x||_p \\geq ||y||_p$ for $1\\leq p \\leq 2$ provided $||x||_1 =||y||_1$. Previously the author proved this kind of property for $p>2$, for certain polynomials $F_{k,r}(x)$ which generalize the $e_k(x)$. In this paper we give two additional generalizations of this type, involving two other families of polynomials. When $x$ consists of the eigenvalues of a matrix $A$, we give a formula for the polynomials in terms of the entries of $A$, generalizing sums of principal $k \\times k$ subdeterminants.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-02-19T02:32:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A30",
      "05E05",
      "15A15"
    ],
    "keywords": [
      "elementary symmetric polynomials",
      "additional generalizations",
      "subdeterminants",
      "eigenvalues"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1302.4506K"
    }
  }
}