{
  "id": "math/0609632",
  "version": "v4",
  "published": "2006-09-22T11:00:16.000Z",
  "updated": "2006-10-19T08:24:44.000Z",
  "title": "A holomorphic map in infinite dimensions",
  "authors": [
    "Seppo I Hiltunen"
  ],
  "comment": "7 pages, LaTeX; v2: a misprint corrected (p. 1, `x' added); v3(=\"v4\"): \" if we fix xi=xi^0, \" added on p. 6",
  "categories": [
    "math.FA"
  ],
  "abstract": "We prove holomorphy E sqcap C(I,varPi) to C(I,varPi) of the map (x,y) mapsto x circ [id,y] where [id,y]:I owns t mapsto (t,y(t)) for a real compact interval I, and where varPi is a complex Banach space and E is a certain locally convex space of continuous functions x:I times varPi to varPi for which x(t,.) is holomorphic for all t in I. We also discuss application of this result to establishing a holomorphic solution map (xi,varphi) mapsto y for functions y:I to varPi satisfying the ordinary differential equation y' = varphi circ [id,y] with initial condition y(t_0) = xi .",
  "revisions": [
    {
      "version": "v4",
      "updated": "2006-10-19T08:24:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46G20"
    ],
    "keywords": [
      "infinite dimensions",
      "holomorphic map",
      "real compact interval",
      "complex banach space",
      "ordinary differential equation"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......9632H"
    }
  }
}