{
  "id": "1110.1554",
  "version": "v2",
  "published": "2011-10-07T14:52:32.000Z",
  "updated": "2012-07-09T13:06:28.000Z",
  "title": "Orthogonal Polynomials on the Sierpinski Gasket",
  "authors": [
    "Kasso A. Okoudjou",
    "Robert S. Strichartz",
    "Elizabeth K. Tuley"
  ],
  "comment": "29 pages, 10 figures, 2 tables. Include short version of previous section 5 in subsection 4.4; correct typos, reduce the number of figures",
  "categories": [
    "math.CA"
  ],
  "abstract": "The construction of a Laplacian on a class of fractals which includes the Sierpinski gasket ({\\bf $SG$}) has given rise to an intensive research on analysis on fractals. For instance, a complete theory of polynomials and power series on $SG$ has been developed by one of us and his coauthors. We build on this body of work to construct certain analogs of classical orthogonal polynomials (OP) on $SG$. In particular, we investigate key properties of these OP on $SG$, including a three-term recursion formula and the asymptotics of the coefficients appearing in this recursion. Moreover, we develop numerical tools that allow us to graph a number of these OP. Finally, we use these numerical tools to investigate the structure of the zero and the nodal sets of these polynomials.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-07-09T13:06:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42C05",
      "28A80",
      "33F05",
      "33A99"
    ],
    "keywords": [
      "sierpinski gasket",
      "three-term recursion formula",
      "numerical tools",
      "complete theory",
      "power series"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1110.1554O"
    }
  }
}