{
  "id": "1307.4277",
  "version": "v1",
  "published": "2013-07-16T13:54:54.000Z",
  "updated": "2013-07-16T13:54:54.000Z",
  "title": "Characterization of derivations through their actions on certain elementary functions",
  "authors": [
    "Eszter Gselmann"
  ],
  "comment": "9 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "The main aim of this note is to provide characterization theorems concerning real derivations. Among others the following implication will be verified: Assume that $\\xi\\colon \\mathbb{R}\\to \\mathbb{R}$ is a given differentiable function and for the additive function $d\\colon \\mathbb{R}\\to \\mathbb{R}$, the mapping \\[ x\\longmapsto d(\\xi(x))-\\xi'(x)d(x) \\] is regular (e. g. measurable, continuous, locally bounded). Then $d$ is a sum of a derivation and a linear function.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-07-16T13:54:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "39B82",
      "39B72"
    ],
    "keywords": [
      "elementary functions",
      "characterization theorems concerning real derivations",
      "linear function",
      "main aim",
      "additive function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1307.4277G"
    }
  }
}