{
  "id": "1612.04802",
  "version": "v1",
  "published": "2016-12-14T20:49:08.000Z",
  "updated": "2016-12-14T20:49:08.000Z",
  "title": "Quaternionic spherical harmonics and a sharp multiplier theorem on quaternionic spheres",
  "authors": [
    "Julian Ahrens",
    "Michael G. Cowling",
    "Alessio Martini",
    "Detlef Müller"
  ],
  "categories": [
    "math.AP",
    "math.FA"
  ],
  "abstract": "A sharp $L^p$ spectral multiplier theorem of Mihlin--H\\\"ormander type is proved for a distinguished sub-Laplacian on quaternionic spheres. This is the first such result on compact sub-Riemannian manifolds where the horizontal space has corank greater than one. The proof hinges on the analysis of the quaternionic spherical harmonic decomposition, of which we present an elementary derivation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-12-14T20:49:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B15",
      "43A85",
      "53C26"
    ],
    "keywords": [
      "sharp multiplier theorem",
      "quaternionic spheres",
      "spectral multiplier theorem",
      "quaternionic spherical harmonic decomposition",
      "compact sub-riemannian manifolds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}