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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Bounding matrix coefficients for smooth vectors of tempered representations


Author: Binyong Sun
Journal: Proc. Amer. Math. Soc. 137 (2009), 353-357
MSC (2000): Primary 22E45; Secondary 22E30
Published electronically: August 6, 2008
MathSciNet review: 2439460
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Abstract: Let $ G$ be a Lie group. Let $ (\pi,V)$ be a unitary representation of $ G$ which is weakly contained in the regular representation. For smooth vectors $ u,v$ in $ V$, we give an upper bound for the matrix coefficient $ \langle \pi(g)u,v\rangle$, in terms of Harish-Chandra's $ \Xi$-function.


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Additional Information

Binyong Sun
Affiliation: Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, People’s Republic of China
Email: sun@math.ac.cn

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09598-1
PII: S 0002-9939(08)09598-1
Received by editor(s): September 7, 2007
Published electronically: August 6, 2008
Additional Notes: This work was supported by the Knowledge Innovation Program of the Chinese Academy of Sciences.
Communicated by: Wen-Ching Winnie Li
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.