More on Modified Spherical Harmonics

Beitrag in einer Fachzeitschrift


Details zur Publikation

Autorinnen und Autoren: Leutwiler H
Zeitschrift: Advances in Applied Clifford Algebras
Jahr der Veröffentlichung: 2019
Band: 29
Heftnummer: 4
ISSN: 0188-7009


Abstract

A modification of the classical theory of spherical harmonics is presented. The space Rd= { (x1, … , xd) } is replaced by the upper half space R+d={(x1,…,xd),xd>0}, and the unit sphere Sd - 1 in Rd 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 Sd - 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.


Zitierweisen

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: 

Zuletzt aktualisiert 2019-07-08 um 10:38