Illinois Journal of Mathematics
- Illinois J. Math.
- Volume 28, Issue 1 (1984), 162-179.
Exponentially bounded positive definite functions
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.
Illinois J. Math., Volume 28, Issue 1 (1984), 162-179.
First available in Project Euclid: 20 October 2009
Permanent link to this document
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. https://projecteuclid.org/euclid.ijm/1256046160