{
  "id": "1510.06259",
  "version": "v1",
  "published": "2015-10-21T14:12:38.000Z",
  "updated": "2015-10-21T14:12:38.000Z",
  "title": "Smoothness of convolution products of orbital measures on rank one compact symmetric spaces",
  "authors": [
    "Kathryn Hare",
    "Jimmy He"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "We prove that all convolution products of pairs of continuous orbital measures in rank one, compact symmetric spaces are absolutely continuous and determine which convolution products are in $L^{2}$ (meaning, their density function is in $L^{2})$. Characterizations of the pairs whose convolution product is either absolutely continuous or in $L^2$ are given in terms of the dimensions of the corresponding double cosets. In particular, we prove that if $G/K$ is not $SU(2)/SO(2),$ then the convolution of any two regular orbital measures is in $L^{2}$, while in $SU(2)/SO(2)$ there are no pairs of orbital measures whose convolution product is in $L^{2}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-10-21T14:12:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "43A80",
      "22E30",
      "53C35"
    ],
    "keywords": [
      "convolution product",
      "compact symmetric spaces",
      "smoothness",
      "regular orbital measures",
      "continuous orbital measures"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151006259H"
    }
  }
}