Generating functions for the spherical functions on some classical Gelfand pairs
type: Item
instance of: scholarly article
title: Generating functions for the spherical functions on some classical Gelfand pairs
zbMATH Open document ID: 0790.43014
author: Shigeru Watanabe
published in: Proceedings of the Japan Academy. Series A
publication date: 1993-01-17T00:00:00Z
review text: It is known that the zonal spherical functions on the unit sphere in real space \(\mathbb{R}^ n\) can be expressed through the Gegenbauer polynomials, and have a generating function which has the form of a power of a trinomial. The purpose of the article is to announce that similar generating functions also exist for the zonal spherical functions in the cases of complex and quaternion spaces \(\mathbb{C}^ n\) and \(\mathbb{H}^ n\).
Mathematics Subject Classification ID: 43A90
Mathematics Subject Classification ID: 33D80
zbMATH DE Number: 97948
zbMATH Keywords: zonal spherical functions
zbMATH Keywords: generating functions
MaRDI profile type: Publication
full work available at URL: pjaa.68.140
OpenAlex ID: W2093407913
cites work: Deux cours d'analyse harmonique. École d'Été d'Analyse Harmonique de Tunis, 1984
cites work: Composition Series and Intertwining Operators for the Spherical Principal Series. I
DOI: 10.3792/PJAA.68.140
description: scientific article; zbMATH DE number 97948