{
  "id": "1307.0634",
  "version": "v1",
  "published": "2013-07-02T09:13:09.000Z",
  "updated": "2013-07-02T09:13:09.000Z",
  "title": "Derivations and linear functions along rational functions",
  "authors": [
    "Eszter Gselmann"
  ],
  "comment": "13 pages; published in Monatshefte f\\\"ur Mathematik in 2013",
  "doi": "10.1007/s00605-012-0375-z",
  "categories": [
    "math.CA"
  ],
  "abstract": "The main purpose of this paper is to give characterization theorems on derivations as well as on linear functions. Among others the following problem will be investigated: Let $n\\in\\mathbb{Z}$, $f, g\\colon\\mathbb{R}\\to\\mathbb{R}$ be additive functions, $<{array}{cc} a&b c&d {array}>\\in\\mathbf{GL}_{2}(\\mathbb{Q})$ be arbitrarily fixed, and let us assume that the mapping \\[ \\phi(x)=g<\\frac{ax^{n}+b}{cx^{n}+d}>-\\frac{x^{n-1}f(x)}{(cx^{n}+d)^{2}} \\quad <x\\in\\mathbb{R}, cx^{n}+d\\neq 0> \\] satisfies some regularity on its domain (e.g. (locally) boundedness, continuity, measurability). Is it true that in this case the above functions can be represented as a sum of a derivation and a linear function? Analogous statements ensuring linearity will also be presented.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-07-02T09:13:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "39B82",
      "39B72"
    ],
    "keywords": [
      "linear function",
      "rational functions",
      "derivation",
      "main purpose",
      "characterization theorems"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1307.0634G"
    }
  }
}