{
  "id": "1607.00930",
  "version": "v1",
  "published": "2016-07-04T15:29:34.000Z",
  "updated": "2016-07-04T15:29:34.000Z",
  "title": "Error in Sobolev norms of orthogonal projection onto polynomials in the unit ball",
  "authors": [
    "Leonardo E. Figueroa"
  ],
  "comment": "10 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "We study approximation properties of weighted $L^2$-orthogonal projectors onto spaces of polynomials of bounded degree in the Euclidean unit ball, where the weight is of the generalized Gegenbauer form $x \\mapsto (1-\\|x\\|^2)^\\alpha$, $\\alpha > -1$. Said properties are measured in Sobolev-type norms in which the same weighted $L^2$ norm is used to control all involved weak derivatives. The method of proof does not rely on any particular basis of orthogonal polynomials, which allows for a streamlined and dimension-independent exposition.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-07-04T15:29:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "41A25",
      "41A10",
      "46E35"
    ],
    "keywords": [
      "orthogonal projection",
      "sobolev norms",
      "study approximation properties",
      "euclidean unit ball",
      "orthogonal polynomials"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}