Quaternionic spherical harmonics and a sharp multiplier theorem on quaternionic spheres

A sharp L p 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 quat...

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Bibliographic Details
Published inMathematische Zeitschrift Vol. 294; no. 3-4; pp. 1659 - 1686
Main Authors Ahrens, Julian, Cowling, Michael G., Martini, Alessio, Müller, Detlef
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.04.2020
Springer Nature B.V
Subjects
Mathematics
Mathematics and Statistics
Riemann manifold
Spherical harmonics
Theorems
Quaternionic sphere
Secondary 53C26
Sub-Laplacian
Spherical harmonic
43A85
Spectral multiplier
Primary 42B15
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Summary:A sharp L p 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.
ISSN:0025-5874
1432-1823
DOI:10.1007/s00209-019-02313-w