Quaternionic spherical harmonics and a sharp multiplier theorem on quaternionic spheres

Julian Ahrens; Michael Cowling; Alessio Martini; Detlef Müller

doi:10.1007/s00209-019-02313-w

Quaternionic spherical harmonics and a sharp multiplier theorem on quaternionic spheres

Julian Ahrens
, Michael Cowling
, Alessio Martini
, Detlef Müller

Mathematics

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

460 Downloads (Pure)

Abstract

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.

Original language	English
Pages (from-to)	1659-1686
Number of pages	28
Journal	Mathematische Zeitschrift
Volume	294
Issue number	3-4
Early online date	15 May 2019
DOIs	https://doi.org/10.1007/s00209-019-02313-w
Publication status	Published - Apr 2020

Keywords

Quaternionic sphere
Spectral multiplier
Spherical harmonic
Sub-Laplacian

ASJC Scopus subject areas

General Mathematics

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10.1007/s00209-019-02313-wLicence: None: All rights reserved

Ahrens_et_al_Quaternionic_spherical_harmonics_Mathematische_Zeitschrift_2019
Checked for eligibility: 12/04/2019 This is a post-peer-review, pre-copyedit version of an article published in Mathematische Zeitschrift. The final authenticated version is available online at: http://dx.doi.org/10.1007/s00209-019-02313-w
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https://link.springer.com/article/10.1007/s00209-019-02313-wLicence: None: All rights reserved

Cite this

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abstract = "A sharp Lp spectral multiplier theorem of Mihlin--H{\"o}rmander 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.",

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AU - Ahrens, Julian

AU - Cowling, Michael

AU - Martini, Alessio

AU - Müller, Detlef

PY - 2020/4

Y1 - 2020/4

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AB - 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.

KW - Quaternionic sphere

KW - Spectral multiplier

KW - Spherical harmonic

KW - Sub-Laplacian

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IS - 3-4

ER -

Quaternionic spherical harmonics and a sharp multiplier theorem on quaternionic spheres

Abstract

Keywords

ASJC Scopus subject areas

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