Proceedings of the American Mathematical Society

The extension of positive definite operator-valued functions defined on a symmetric interval of an ordered group

Author(s): Mihály Bakonyi
Journal: Proc. Amer. Math. Soc. 130 (2002), 1401-1406.
MSC (1991): Primary 43A35, 47A57, 42A70, 47A20
Posted: October 12, 2001
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Abstract: Let

be an ordered abelian group and $a\in G_1$ . Let

be an abelian group and

an operator-valued positive definite function on $(-a,a)\times G_2$ . We prove that

admits a positive definite extension to $G_1\times G_2$ , generalizing in this way existing results for the case when $G_1=\mathbf{R}$ and

is continuous.

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