{
  "id": "1404.0263",
  "version": "v1",
  "published": "2014-04-01T14:46:06.000Z",
  "updated": "2014-04-01T14:46:06.000Z",
  "title": "Characterization of Classes of Polynomial Functions",
  "authors": [
    "J. M. Almira",
    "L. Székelyhidi"
  ],
  "comment": "7 pages, submitted to a Journal. arXiv admin note: text overlap with arXiv:1403.4486",
  "categories": [
    "math.FA"
  ],
  "abstract": "In this paper some classes of local polynomial functions on abelian groups are characterized by the properties of their variety. For this characterization we introduce a numerical quantity depending on the variety of the local polynomial only. Moreover, we show that the known characterization of polynomials among generalized polynomials can be simplified: a generalized polynomial is a polynomial if and only if its variety contains finitely many linearly independent additive functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-04-01T14:46:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "characterization",
      "local polynomial functions",
      "generalized polynomial",
      "linearly independent additive functions",
      "abelian groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1404.0263A"
    }
  }
}