{
  "id": "1503.04786",
  "version": "v1",
  "published": "2015-03-16T19:41:53.000Z",
  "updated": "2015-03-16T19:41:53.000Z",
  "title": "Darboux transformations for multivariate orthogonal polynomials",
  "authors": [
    "Gerardo Ariznabarreta",
    "Manuel Mañas"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:1409.0570",
  "categories": [
    "math.CA"
  ],
  "abstract": "Darboux transformations for polynomial perturbations of a real multivariate measure are found. The 1D Christoffel formula is extended to the multidimensional realm: multivariate orthogonal polynomials are expressed in terms of last quasi-determinants and sample matrices. The coefficients of these matrices are the original orthogonal polynomials evaluated at a set of nodes, which is supposed to be poised. A discussion for the existence of poised sets and geometrically poised sets is given in terms of algebraic varieties in the complex affine space.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-03-16T19:41:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J70",
      "15A23",
      "33C45",
      "37K10",
      "37L60",
      "42C05",
      "46L55"
    ],
    "keywords": [
      "multivariate orthogonal polynomials",
      "darboux transformations",
      "complex affine space",
      "1d christoffel formula",
      "poised sets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150304786A"
    }
  }
}