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

 

On the degree of rapid decay


Author: Bogdan Nica
Journal: Proc. Amer. Math. Soc. 138 (2010), 2341-2347
MSC (2010): Primary 20F99, 22D15, 46E39
Published electronically: March 4, 2010
MathSciNet review: 2607863
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Abstract: A finitely generated group $ \Gamma$ equipped with a word-length is said to satisfy property RD if there are $ C, s\geq 0$ such that, for all non-negative integers $ n$, we have $ \Vert a\Vert\leq C (1+n)^s \Vert a\Vert _2$ whenever $ a\in\mathbb{C}\Gamma$ is supported on elements of length at most $ n$.

We show that, for infinite $ \Gamma$, the degree $ s$ is at least $ 1/2$.


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Additional Information

Bogdan Nica
Affiliation: Department of Mathematics, Vanderbilt University, Nashville, Tennessee 37240
Address at time of publication: Department of Mathematics and Statistics, University of Victoria, Victoria, BC, Canada V8W 3R4

DOI: http://dx.doi.org/10.1090/S0002-9939-10-10289-5
PII: S 0002-9939(10)10289-5
Received by editor(s): August 22, 2009
Received by editor(s) in revised form: November 12, 2009
Published electronically: March 4, 2010
Communicated by: Varghese Mathai
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.