Decay of eigenfunctions on semisimple symmetric spaces
type: Item
instance of: scholarly article
title: Decay of eigenfunctions on semisimple symmetric spaces
zbMATH Open document ID: 0789.22020
DOI: 10.1215/S0012-7094-91-06423-9
author: Henrik Schlichtkrull
author: Zeév Rudnick
published in: Duke Mathematical Journal
publication date: 1992-09-27T00:00:00Z
review text: Let \(G\) be a connected semisimple real Lie group with finite center, \(\sigma\) an involution of \(G\), and \(H\) an open subgroup of the fixed point set of \(\sigma\). Let \(\theta\) be a Cartan involution of \(G\) commuting with \(\sigma\), \(K\) the corresponding maximal compact subgroup. Let \(f \in C^ \infty(G/H)\) be a left \(K\)-finite eigenfunction of \(Z( {\mathfrak g})\). The authors assume that the \(({\mathfrak g},K)\)-module \(V_ f\) generated by \(f\) is unitarizable and that its restriction to any noncompact factor of \(G\) does not contain the trivial representation. Then the authors prove that \(f\) vanishes at infinity on \(G/H\) and give rates of decay for \(f\), depending on the Langlands parameters of \(V_ f\).
Mathematics Subject Classification ID: 22E30
Mathematics Subject Classification ID: 43A85
zbMATH DE Number: 58535
zbMATH Keywords: decay of eigenfunctions
zbMATH Keywords: semisimple real Lie group
reviewed by: Paul Godin
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 58535