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Extensions of Positive Definite Functions on Amenable Groups

Published online by Cambridge University Press:  20 November 2018

M. Bakonyi  and
D. Timotin
M. Bakonyi
Affiliation:
Department of Mathematics and Statistics, Georgia State University, Atlanta, GA, U.S.A.e-mail: [email protected]
D. Timotin
Affiliation:
Institute of Mathematics of the Romanian Academy, Bucharest, Romaniae-mail: [email protected]
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Abstract

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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.

Keywords

43A3547A5720E05
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 54 , Issue 1 , 01 March 2011 , pp. 3 - 11
Copyright
Copyright © Canadian Mathematical Society 2011

References

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