Geodesic
Extensions of Positive Definite Functions on Amenable Groups
Canadian mathematical bulletin, Tome 54 (2011) no. 1, pp. 3-11

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DOI

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.
DOI : 10.4153/CMB-2010-081-0
Mots-clés : 43A35, 47A57, 20E05 
Bakonyi, M.; Timotin, D. Extensions of Positive Definite Functions on Amenable Groups. Canadian mathematical bulletin, Tome 54 (2011) no. 1, pp. 3-11. doi: 10.4153/CMB-2010-081-0
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     title = {Extensions of {Positive} {Definite} {Functions} on {Amenable} {Groups}},
     journal = {Canadian mathematical bulletin},
     pages = {3--11},
     year = {2011},
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     number = {1},
     doi = {10.4153/CMB-2010-081-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2010-081-0/}
}
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