{
  "id": "1201.0297",
  "version": "v2",
  "published": "2011-12-31T18:14:53.000Z",
  "updated": "2012-01-09T17:11:03.000Z",
  "title": "Convolution and involution on function spaces of homogeneous spaces",
  "authors": [
    "Arash Ghaani Farashahi"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "Let $G$ be a locally compact group and also let $H$ be a compact subgroup of $G$. It is shown that, if $\\mu$ is a relatively invariant measure on $G/H$ then there is a well-defined convolution on $L^1(G/H,\\mu)$ such that the Banach space $L^1(G/H,\\mu)$ becomes a Banach algebra. We also find a generalized definition of this convolution for other $L^p$-spaces. Finally, we show that various types of involutions can be considered on $G/H$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-01-09T17:11:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "43A15",
      "43A85"
    ],
    "keywords": [
      "function spaces",
      "homogeneous spaces",
      "involution",
      "banach algebra",
      "relatively invariant measure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1201.0297G"
    }
  }
}