{
  "id": "2002.01638",
  "version": "v1",
  "published": "2020-02-05T04:57:12.000Z",
  "updated": "2020-02-05T04:57:12.000Z",
  "title": "Orthogonal polynomial projection error in Dunkl-Sobolev norms in the ball",
  "authors": [
    "Gonzalo A. Benavides",
    "Leonardo E. Figueroa"
  ],
  "comment": "27 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "We study approximation properties of weighted $\\mathrm{L}^2$-orthogonal projectors onto spaces of polynomials of bounded degree in the Euclidean unit ball, where the weight is of the reflection-invariant form $(1-\\lVert x \\rVert^2)^\\alpha \\prod_{i=1}^d \\lvert x_i \\rvert^{\\gamma_i}$, $\\alpha, \\gamma_1, \\dots, \\gamma_d > -1$. Said properties are measured in Dunkl-Sobolev-type norms in which the same weighted $\\mathrm{L}^2$ norm is used to control all the involved differential-difference Dunkl operators, such as those appearing in the Sturm-Liouville characterization of similarly weighted $\\mathrm{L}^2$-orthogonal polynomials, as opposed to the partial derivatives of Sobolev-type norms. The method of proof relies on spaces instead of bases of orthogonal polynomials, which greatly simplifies the exposition.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-02-05T04:57:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "41A25",
      "41A10",
      "46E35",
      "33C52"
    ],
    "keywords": [
      "orthogonal polynomial projection error",
      "dunkl-sobolev norms",
      "euclidean unit ball",
      "study approximation properties",
      "differential-difference dunkl operators"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}