Illinois Journal of Mathematics

Exponentially bounded positive definite functions

Christian Berg and P. H. Maserick

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Equivalent conditions for scalar (or operator valued) positive definite functions, on a commutative semigroup $S$ with identity $e$, to admit a disintegration with respect to a regular positive (operator valued) measure supported by an arbitrary compact subset of semicharacters are given. The theory links to the theory of $\tau$-positive functions presented previously by the second author and comparisons between the two are given. Old and new theorems to classical and modern moment problems are obtained as a consequence.

Article information

Illinois J. Math., Volume 28, Issue 1 (1984), 162-179.

First available in Project Euclid: 20 October 2009

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 43A35: Positive definite functions on groups, semigroups, etc.
Secondary: 22A20: Analysis on topological semigroups 46N05


Berg, Christian; Maserick, P. H. Exponentially bounded positive definite functions. Illinois J. Math. 28 (1984), no. 1, 162--179. doi:10.1215/ijm/1256046160.

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