Wave packets for the relative discrete series. II: The nonholomorphic case
type: Item
instance of: scholarly article
title: Wave packets for the relative discrete series. II: The nonholomorphic case
zbMATH Open document ID: 0625.22011
DOI: 10.1016/0022-1236(87)90058-9
author: Rebecca A. Herb
author: Joseph A. Wolf
published in: Journal of Functional Analysis
publication date: 1987-01-01T00:00:00Z
review text: This paper continues the investigations of the authors in the harmonic analysis on semisimple Lie groups without the finiteness condition for the center [see, for example, Compos. Math. 57, 271-355 (1986; Zbl 0587.22005)]. Let G be a connected simple Lie group with infinite center, K be a maximal compactly embedded subgroup. (Then G is simply connected and G/K is a Hermitian symmetric space.) In this paper wave packets of K- finite matrix elements of relative discrete series representations are constructed by the integration on bounded intervals which parametrize this series [the case of unbounded intervals is considered in the first part of this work (see the preceding review)]. The main result of the paper is that linear combinations of all these wave packets form a dense subspace of the space of cusp forms. This is the analogue of Harish-Chandra's result for groups with finite center. On the other hand, it is proved that one cannot expect a direct analogue of Harish-Chandra's theorem about the decomposition of the Schwartz space.
Mathematics Subject Classification ID: 22E30
Mathematics Subject Classification ID: 43A80
Mathematics Subject Classification ID: 46A13
Mathematics Subject Classification ID: 46A11
zbMATH DE Number: 4015036
zbMATH Keywords: matrix coefficients
zbMATH Keywords: harmonic analysis on semisimple Lie groups
zbMATH Keywords: infinite center
zbMATH Keywords: Hermitian symmetric space
zbMATH Keywords: wave packets
zbMATH Keywords: finite matrix elements
zbMATH Keywords: relative discrete series
zbMATH Keywords: cusp forms
zbMATH Keywords: Schwartz space
reviewed by: V. F. Molchanov
MaRDI profile type: Publication
full work available at URL: 0022-1236(87)90058-9
OpenAlex ID: W4243745464
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description: scientific article; zbMATH DE number 4015036