Clifford analysis techniques for spherical PDE.
type: Item
instance of: scholarly article
title: Clifford analysis techniques for spherical PDE.
zbMATH Open document ID: 1047.53023
author: N. Delaunay
published in: The Journal of Fourier Analysis and Applications
publication date: 2003-10-13T00:00:00Z
review text: The present paper investigates \(\alpha\)-order spherical harmonic functions on a sphere with respect to the spherical Laplace-Beltrami operator of order \(\alpha\), i.e. LB + a suitable constant term depending on \(\alpha\). The authors obtain explicit Green-type integral formulae in terms of Gegenbauer functions. They proceed and extend their treatment to higher-order spherical Dirac-type operators, giving intertwining formulae via the Cayley transformation with their Euclidean counterparts. These heavy tasks are performed using the full force of Clifford analysis, which allows factorization of operators in terms of lower-order ones; this being in general impossible within the classical analytical framework. The paper is clearly written and paves the way for further developments in the field, already envisaged by the authors.
reviewed by: Mauro Spera
Mathematics Subject Classification ID: 53C27
Mathematics Subject Classification ID: 30G35
Mathematics Subject Classification ID: 31B05
zbMATH DE Number: 1921136
zbMATH Keywords: spherical harmonic functions
zbMATH Keywords: integral formulae
zbMATH Keywords: Clifford analysis
MaRDI profile type: Publication
full work available at URL: s00041-002-0026-1
OpenAlex ID: W2023720823
DOI: 10.1007/S00041-002-0026-1
description: scientific article; zbMATH DE number 1921136