Quaternionic spherical harmonics and a sharp multiplier theorem on quaternionic spheres

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External organisations

  • UNSW Sydney
  • Deutsches Forschungszentrum für Künstliche Intelligenz
  • University of Kiel


A sharp Lp spectral multiplier theorem of Mihlin--Hörmander 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.


Original languageEnglish
Pages (from-to)1659-1686
JournalMathematische Zeitschrift
Issue number3-4
Early online date15 May 2019
Publication statusPublished - Apr 2020


  • Quaternionic sphere, Spectral multiplier, Spherical harmonic, Sub-Laplacian

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