More on Modified Spherical Harmonics

Leutwiler H (2019)

Publication Type: Journal article

Publication year: 2019

Journal

Advances in Applied Clifford Algebras Springer Verlag (Germany)

Book Volume: 29

Article Number: 70

Journal Issue: 4

DOI: 10.1007/s00006-019-0990-z

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+k∂u∂xd=0, for k∈ N. 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 k= d- 2 the modified theory has already been treated by the author.

How to cite

APA:

Leutwiler, H. (2019). More on Modified Spherical Harmonics. Advances in Applied Clifford Algebras, 29(4). https://dx.doi.org/10.1007/s00006-019-0990-z

MLA:

Leutwiler, Heinz. "More on Modified Spherical Harmonics." Advances in Applied Clifford Algebras 29.4 (2019).

BibTeX: Download