Bessel functions associated with representations of formally real Jordan algebras
type: Item
instance of: scholarly article
title: Bessel functions associated with representations of formally real Jordan algebras
zbMATH Open document ID: 0612.43009
DOI: 10.1016/0022-1236(87)90019-X
author: Giancarlo Travaglini
author: Jacques Faraut
published in: Journal of Functional Analysis
publication date: 1987-01-01T00:00:00Z
review text: Let U be a formally real Jordan algebra, E a Euclidean space, \(\phi\) : \(U\to Sym^+(E)\) a representation of U, where \(Sym^+(E)\) denotes the real linear space of all symmetric endomorphisms of E equipped with the Jordan product \(A\circ B=(AB+BA)\). Denote by Q(\(\xi)\) the corresponding vector-valued quadratic form and by \(\Sigma\) the Stiefel manifold \(\{\xi\in E:\) \(Q(\xi)=e\}\), where e is the identity of U. The authors introduce generalized Bessel functions \[ J(r,s)=\int_{\Sigma}\exp \{-i (\phi (r^{1/2})\sigma, \phi (s^{1/2})\sigma_ 0)\quad d\beta (\sigma)\quad, \] where \(\beta\) is the Riemannian volume form on \(\Sigma\). They extend the classical results of radial Fourier analysis to this case and prove an asymptotic formula.
Mathematics Subject Classification ID: 43A99
Mathematics Subject Classification ID: 33C10
Mathematics Subject Classification ID: 17C10
Mathematics Subject Classification ID: 43A32
Mathematics Subject Classification ID: 43A65
zbMATH DE Number: 3990055
zbMATH Keywords: formally real Jordan algebra
zbMATH Keywords: generalized Bessel functions
zbMATH Keywords: radial Fourier analysis
zbMATH Keywords: asymptotic formula
reviewed by: Sh. A. Ayupov
MaRDI profile type: Publication
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full work available at URL: 0022-1236(87)90019-x
OpenAlex ID: W2045164423
description: scientific article; zbMATH DE number 3990055