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Extensions of Positive Definite Functions on Amenable Groups

  Published:2010-08-03
 Printed: Mar 2011
  • M. Bakonyi,
    Department of Mathematics and Statistics, Georgia State University, Atlanta, GA, U.S.A
  • D. Timotin,
    Institute of Mathematics of the Romanian Academy, Bucharest, Romania
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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, 47A57, 20E05 show english descriptions Positive definite functions on groups, semigroups, etc.
Operator methods in interpolation, moment and extension problems [See also 30E05, 42A70, 42A82, 44A60]
Free nonabelian groups
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
 

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