On the asymptotics of the Bochner-Riesz kernel on compact Lie groups
type: Item
instance of: scholarly article
title: On the asymptotics of the Bochner-Riesz kernel on compact Lie groups
zbMATH Open document ID: 0615.43006
DOI: 10.1016/0022-1236(86)90104-7
published in: Journal of Functional Analysis
publication date: 1986-01-01T00:00:00Z
review text: On sait que, sur le tore \(T^ n\), le noyau de Bochner-Riesz défini par \[ D_ R^{\delta} = \sum_{| m| \leq R}(1-(| m| /R)^ 2)^{\delta}\quad e^{imx} \] admet une norme \(L^ 1\) qui est de l'ordre de \(R^{(n-1)/2-\delta}\) lorsque \(0\leq \delta <(n-1)/2\), et de l'ordre de log R lorsque \(\delta =(n-1)/2.\) Ce résultat est généralisé ici à tout groupe de Lie compact connexe de dimension n, à l'aide d'une formule sommatoire de Poisson pour les fonctions centrales de G.
Mathematics Subject Classification ID: 43A75
Mathematics Subject Classification ID: 22E30
zbMATH DE Number: 3996343
zbMATH Keywords: compact Lie groups
zbMATH Keywords: Bochner-Riesz kernel
zbMATH Keywords: Poisson summation formula
author: Bernd Dreseler
reviewed by: Noël Leblanc
MaRDI profile type: Publication
full work available at URL: 0022-1236(86)90104-7
OpenAlex ID: W2043953399
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description: scientific article; zbMATH DE number 3996343