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Extensions of Positive Definite Functions on Amenable Groups
Published online by Cambridge University Press: 20 November 2018
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.
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- Research Article
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- Copyright © Canadian Mathematical Society 2011
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