Modified Spherical Harmonics in Several Dimensions

Leutwiler H (2019)

Publication Type: Journal article

Publication year: 2019

Journal

Advances in Applied Clifford Algebras Springer Verlag (Germany)

Book Volume: 29

Article Number: 100

Journal Issue: 5

DOI: 10.1007/s00006-019-1021-9

Abstract

A modification of the classical theory of spherical harmonics is presented. The space R^d= { (x1, … , xd) } is replaced by the upper half space R+d={(x1,…,xd),xd>0}, and the unit sphere S^d ^- ¹ in R^d by the unit half sphere S+d-1={(x1,…,xd):x12+⋯+xd2=1,xd>0}. Instead of the Laplace equation Δ h= 0 we shall consider the Weinstein equation xdΔu+(d-2)∂u∂xd=0. The Euclidean scalar product for functions on S^d ^- ¹ will be replaced by a non-Euclidean one for functions on S+d-1. It will be shown that in this modified setting all major results from the theory of spherical harmonics stay valid. In case d= 3 and d= 4 the modified theory has already been treated.

Additional Organisation(s)

Lehrstuhl für Partial Differential Equations

How to cite

APA:

Leutwiler, H. (2019). Modified Spherical Harmonics in Several Dimensions. Advances in Applied Clifford Algebras, 29(5). https://dx.doi.org/10.1007/s00006-019-1021-9

MLA:

Leutwiler, Heinz. "Modified Spherical Harmonics in Several Dimensions." Advances in Applied Clifford Algebras 29.5 (2019).

BibTeX: Download