{
  "id": "1706.09045",
  "version": "v1",
  "published": "2017-06-21T16:01:20.000Z",
  "updated": "2017-06-21T16:01:20.000Z",
  "title": "Series Analysis and Schwartz Algebras of Spherical Convolutions on Semisimple Lie Groups",
  "authors": [
    "Olufemi O. Oyadare"
  ],
  "comment": "19 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "We give the exact contributions of Harish-Chandra transform, $(\\mathcal{H}f)(\\lambda),$ of Schwartz functions $f$ to the harmonic analysis of spherical convolutions and the corresponding $L^{p}-$ Schwartz algebras on a connected semisimple Lie group $G$ (with finite center). One of our major results gives the proof of how the Trombi-Varadarajan Theorem enters into the spherical convolution transform of $L^{p}-$ Schwartz functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-06-21T16:01:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "43A85",
      "22E30",
      "22E46"
    ],
    "keywords": [
      "schwartz algebras",
      "series analysis",
      "schwartz functions",
      "trombi-varadarajan theorem enters",
      "connected semisimple lie group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}