{
  "id": "1009.3921",
  "version": "v3",
  "published": "2010-09-20T19:38:40.000Z",
  "updated": "2013-12-18T21:59:55.000Z",
  "title": "Operator monotone functions and Löwner functions of several variables",
  "authors": [
    "Jim Agler",
    "John E. McCarthy",
    "Nicholas J. Young"
  ],
  "journal": "Annals of Mathematics (2) 176 [2012] no. 3, 1783-1826",
  "categories": [
    "math.FA",
    "math.CV"
  ],
  "abstract": "We prove generalizations of L\\\"owner's results on matrix monotone functions to several variables. We give a characterization of when a function of $d$ variables is locally monotone on $d$-tuples of commuting self-adjoint $n$-by-$n$ matrices. We prove a generalization to several variables of Nevanlinna's theorem describing analytic functions that map the upper half-plane to itself and satisfy a growth condition. We use this to characterize all rational functions of two variables that are operator monotone.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-12-18T21:59:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A63",
      "32A35"
    ],
    "keywords": [
      "operator monotone functions",
      "löwner functions",
      "nevanlinnas theorem describing analytic functions",
      "matrix monotone functions",
      "growth condition"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Princeton University and the Institute for Advanced Study",
      "journal": "Ann. Math."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1009.3921A"
    }
  }
}