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

Author: Mihály Bakonyi
Journal: Proc. Amer. Math. Soc. 130 (2002), 1401-1406
MSC (1991): Primary 43A35, 47A57, 42A70, 47A20
Published electronically: October 12, 2001
MathSciNet review: 1879963
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Abstract: Let $G_1$ be an ordered abelian group and $a\in G_1$. Let $G_2$ be an abelian group and $f$ an operator-valued positive definite function on $(-a,a)\times G_2$. We prove that $f$ 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 $f$ is continuous.

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Additional Information

Mihály Bakonyi
Affiliation: Department of Mathematics, Georgia State University, Atlanta, Georgia 30303

Received by editor(s): November 14, 2000
Published electronically: October 12, 2001
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2001 American Mathematical Society