Quaternionic spherical harmonics and a sharp multiplier theorem on quaternionic spheres

Research output: Contribution to journalArticle

Authors

Colleges, School and Institutes

External organisations

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

Abstract

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.

Details

Original languageEnglish
Pages (from-to)1659-1686
JournalMathematische Zeitschrift
Volume294
Issue number3-4
Early online date15 May 2019
Publication statusPublished - Apr 2020

Keywords

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

ASJC Scopus subject areas