{
  "id": "math/0406569",
  "version": "v1",
  "published": "2004-06-28T10:50:28.000Z",
  "updated": "2004-06-28T10:50:28.000Z",
  "title": "Limits of functions and elliptic operators",
  "authors": [
    "Siddhartha Gadgil"
  ],
  "comment": "6 pages, no figures, no tables",
  "journal": "Proc. Indian Acad. Sci. (Math. Sci.), Vol. 114, No. 2, May 2004, pp. 153-158",
  "categories": [
    "math.DG"
  ],
  "abstract": "We show that a subspace $S$ of the space of real analytical functions on a manifold that satisfies certain regularity properties is contained in the set of solutions of a linear elliptic differential equation. The regularity properties are that $S$ is closed in $L^2(M)$ and that if a sequence of functions $f_n$ in $S$ converges in $L^2(M)$, then so do the partial derivatives of the functions $f_n$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-06-28T10:50:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58J05",
      "32C05"
    ],
    "keywords": [
      "elliptic operators",
      "linear elliptic differential equation",
      "regularity properties",
      "real analytical functions",
      "partial derivatives"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......6569G"
    }
  }
}