{
  "id": "math/0603186",
  "version": "v1",
  "published": "2006-03-08T13:53:14.000Z",
  "updated": "2006-03-08T13:53:14.000Z",
  "title": "Extension of Bernstein Polynomials to Infinite Dimensional Case",
  "authors": [
    "Lorenzo D'Ambrosio"
  ],
  "comment": "14 pages. to appear on Journal of Approximation Theory",
  "journal": "Journal of Approximation Theory 140 (2006) 191 - 202",
  "doi": "10.1016/j.jat.2005.12.006",
  "categories": [
    "math.FA",
    "math.CA"
  ],
  "abstract": "The purpose of this paper is to study some new concrete approximation processes for continuous vector-valued mappings defined on the infinite dimensional cube or on a subset of a real Hilbert space. In both cases these operators are modelled on classical Bernstein polynomials and represent a possible extension to an infinite dimensional setting. The same idea is generalized to obtain from a given approximation process for function defined on a real interval a new approximation process for vector-valued mappings defined on subsets of a real Hilbert space.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-03-08T13:53:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "41A10",
      "41A36",
      "25E15"
    ],
    "keywords": [
      "infinite dimensional case",
      "real hilbert space",
      "vector-valued mappings",
      "infinite dimensional cube",
      "concrete approximation processes"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......3186D"
    }
  }
}