{
  "id": "2004.08727",
  "version": "v1",
  "published": "2020-04-18T23:04:05.000Z",
  "updated": "2020-04-18T23:04:05.000Z",
  "title": "Intertwining operator associated to symmetric groups and summability on the unit sphere",
  "authors": [
    "Yuan Xu"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "An integral representation of the intertwining operator for the Dunkl operators associated with symmetric groups is derived for the class of functions of a single component. The expression provides a closed form formula for the reproducing kernels of $h$-harmonics associated with symmetric groups when one of the components is a coordinate vector. The latter allows us to establish a sharp result for the Ces\\`aro summability of $h$-harmonic series on the unit sphere.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-04-18T23:04:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33C52",
      "42C05",
      "42B08",
      "44A30"
    ],
    "keywords": [
      "symmetric groups",
      "unit sphere",
      "intertwining operator",
      "summability",
      "harmonic series"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}