 |
|
Extensions of Positive Definite Functions on Amenable Groups |
Canad. Math. Bull. 54(2011), 3-11
Published:2010-08-03
Printed: Mar 2011
Printed: Mar 2011
- M. Bakonyi,
- D. Timotin,
Abstract
Let $S$ be a subset of an amenable group $G$ such that $e\in S$ and
$S^{-1}=S$. The main result of this paper states that if the Cayley
graph of $G$ with respect to $S$ has a certain combinatorial property,
then every positive definite operator-valued function on $S$ can be
extended to a positive definite function on $G$. Several known
extension results are obtained as corollaries. New applications are
also presented.
| MSC Classifications: |
43A35 - Positive definite functions on groups, semigroups, etc. 47A57 - Operator methods in interpolation, moment and extension problems [See also 30E05, 42A70, 42A82, 44A60] 20E05 - Free nonabelian groups |