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Available in print format 		Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(e) ISSN 0002-9939(p)

     

Bounding matrix coefficients for smooth vectors of tempered representations

Author(s): Binyong Sun
Journal: Proc. Amer. Math. Soc. 137 (2009), 353-357.
MSC (2000): Primary 22E45; Secondary 22E30
Posted: August 6, 2008
MathSciNet review: 2439460
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Abstract | References | Similar articles | Additional information

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.

References:

1.
M. Cowling, U. Haagerup and R. Howe, Almost $ L^{2}$ matrix coefficients. J. Reine Angew. Math. 387 (1988), 97-110. MR 946351 (89i:22008)

2.
A. Ichino and T. Ikeda, On the periods of automorphic forms on special orthogonal groups and the Gross-Prasad conjecture, preprint.

3.
N. Wallach, Real Reductive Groups I, Academic Press, San Diego, 1988. MR 929683 (89i:22029)

4.
G. Warner, Harmonic Analysis on Semi-simple Lie Groups I, Springer-Verlag, New York, 1972. MR 0498999 (58:16979)

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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: 10.1090/S0002-9939-08-09598-1
PII: S 0002-9939(08)09598-1
Received by editor(s): September 7, 2007
Posted: 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
Copyright of article: Copyright 2008, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.




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