Quaternionic spherical harmonics and a sharp multiplier theorem on quaternionic spheres
Analysis of PDEs
2020-09-15 v2 Functional Analysis
Abstract
A sharp 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.
Cite
@article{arxiv.1612.04802,
title = {Quaternionic spherical harmonics and a sharp multiplier theorem on quaternionic spheres},
author = {Julian Ahrens and Michael G. Cowling and Alessio Martini and Detlef Müller},
journal= {arXiv preprint arXiv:1612.04802},
year = {2020}
}