Harmonic analysis on vector bundles over \(\text{Sp}(1,n)/\text{Sp}(1)\times\text{Sp}(n)\)
type: Item
instance of: scholarly article
title: Harmonic analysis on vector bundles over \(\text{Sp}(1,n)/\text{Sp}(1)\times\text{Sp}(n)\)
zbMATH Open document ID: 0967.43005
author: Angela Pasquale
author: Gerrit van Dijk
published in: L'Enseignement Mathématique. 2e Série
publication date: 2001-01-30T00:00:00Z
review text: A natural generalization of the harmonic analysis over Riemannian symmetric spaces is to consider (sections of) equivariant vector bundles over such spaces. Some methods of the function case carry over, others have to be modified, some reinvented. In the present paper the authors consider bundles over \(Sp(1,n)/Sp(1)\times Sp(n)\) given by irreducible representations of \(Sp(1)\). They use Godement's approach of trace spherical functions which they write in terms of Jacobi functions. They give an explicit inversion formula for the Abel transform, the Paley-Wiener theorem, and the Plancherel theorem for the \(\tau\)-spherical transform. The methods are rooted in the work of Godement and Harish-Chandra, but are kept explicit and down to earth here to make the work accessible to a broader audience.
reviewed by: Anton Deitmar
Mathematics Subject Classification ID: 43A85
Mathematics Subject Classification ID: 22E46
Mathematics Subject Classification ID: 33C80
Mathematics Subject Classification ID: 43A90
zbMATH DE Number: 1558743
zbMATH Keywords: harmonic analysis
zbMATH Keywords: Riemannian symmetric spaces
zbMATH Keywords: equivariant vector bundles
zbMATH Keywords: trace spherical functions
zbMATH Keywords: inversion formula
zbMATH Keywords: Abel transform
zbMATH Keywords: Paley-Wiener theorem
zbMATH Keywords: Plancherel theorem
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1558743