Extensions of positive definite functions on amenable groups

Details Extensions of positive definite functions on amenable groups Extensions of positive definite functions on amenable groups

2008-08-08

arxiv.org/abs/0808.1273v1

Mathematics

Functional Analysis

Scientific paper

Let $S$ be a subset of a amenable group $G$ such that $e\in S$ and $S^{-1}=S$. The main result of the 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 a corollary. New applications are also presented.

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