On the degree of rapid decay

Details On the degree of rapid decay On the degree of rapid decay

2009-11-16

arxiv.org/abs/0911.2944v2

Proceedings of the American Mathematical Society 138 (2010), 2341 - 2347

Mathematics

Group Theory

6 pages, final version

Scientific paper

A finitely generated group $\G$ 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 $\|a\|\leq C (1+n)^s \|a\|_2$ whenever $a\in\C\G$ is
supported on elements of length at most $n$.
We show that, for infinite $\G$, the degree $s$ is at least 1/2.

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