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


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.


Leutwiler, H. (2019). More on Modified Spherical Harmonics. Advances in Applied Clifford Algebras, 29(4).

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


Zuletzt aktualisiert 2019-07-08 um 10:38