{
  "id": "1011.4613",
  "version": "v1",
  "published": "2010-11-20T20:58:13.000Z",
  "updated": "2010-11-20T20:58:13.000Z",
  "title": "Approximation of functions and their derivatives by analytic maps on certain Banach spaces",
  "authors": [
    "D. Azagra",
    "R. Fry",
    "L. Keener"
  ],
  "comment": "17 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "Let X be a separable Banach space which admits a separating polynomial; in particular X a separable Hilbert space. Let $f:X \\rightarrow R$ be bounded, Lipschitz, and $C^1$ with uniformly continuous derivative. Then for each {\\epsilon}>0, there exists an analytic function $g:X \\rightarrow R$ with $|g-f|<\\epsilon$ and $||g'-f'||<\\epsilon$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-11-20T20:58:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "analytic maps",
      "approximation",
      "derivative",
      "separable banach space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1011.4613A"
    }
  }
}