{
  "id": "1705.10193",
  "version": "v1",
  "published": "2017-05-25T19:20:48.000Z",
  "updated": "2017-05-25T19:20:48.000Z",
  "title": "Asymptotic behaviour of the Christoffel functions on the Unit Ball in the presence of a Mass on the Sphere",
  "authors": [
    "Clotilde Martínez",
    "Miguel A. Piñar"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:1512.01064",
  "categories": [
    "math.CA"
  ],
  "abstract": "We present a family of mutually orthogonal polynomials on the unit ball with respect to an inner product which includes a mass uniformly distributed on the sphere. First, connection formulas relating these multivariate orthogonal polynomials and the classical ball polynomials are obtained. Then, using the representation formula for these polynomials in terms of spherical harmonics analytic properties will be deduced. Finally, we analyze the asymptotic behaviour of the Christoffel functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-05-25T19:20:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33C50",
      "42C10"
    ],
    "keywords": [
      "unit ball",
      "christoffel functions",
      "asymptotic behaviour",
      "multivariate orthogonal polynomials",
      "spherical harmonics analytic properties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}