Abstract
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.
Citation
Christian Berg. P. H. Maserick. "Exponentially bounded positive definite functions." Illinois J. Math. 28 (1) 162 - 179, Spring 1984. https://doi.org/10.1215/ijm/1256046160
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