Order estimates for irreducible projections in \(L^ 2\) of a nilmanifold
type: Item
instance of: scholarly article
title: Order estimates for irreducible projections in \(L^ 2\) of a nilmanifold
zbMATH Open document ID: 0569.22008
DOI: 10.1016/0022-1236(85)90026-6
published in: Journal of Functional Analysis
publication date: 1985-01-01T00:00:00Z
review text: Let \(\pi\) be an irreducible representation occuring in \(L^ 2(\Gamma \setminus N)\) where N is a connected, simply connected, nilpotent Lie group and \(\Gamma\) a discrete, cocompact subgroup of N. It is known that the projection onto any irreducible \(\pi\)-summand in \(L^ 2(\Gamma \setminus N)\) is given by convolution against a distribution \(D_{\pi}.\) The main theorem is an estimate of the order of \(D_{\pi}\) in terms of ''canonical objects'' associated to elements of the Kirillov orbit of \(\pi\). The author states that the main ''standard'' examples for irreducibles in \(L^ 2(\Gamma \setminus N)\) are covered by the theorem and the earlier paper by \textit{L. Corwin}, F. P. Greenleaf and \textit{R. Penney} [Commun. Pure Appl. Math. 30, 355-372 (1977; Zbl 0343.22009)].
Mathematics Subject Classification ID: 22E27
zbMATH DE Number: 3908723
zbMATH Keywords: nilpotent Lie group
zbMATH Keywords: Kirillov orbit
author: Lawrence J. Corwin
reviewed by: Henrik Stetkær
MaRDI profile type: Publication
full work available at URL: 0022-1236(85)90026-6
OpenAlex ID: W2019176880
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description: scientific article; zbMATH DE number 3908723