Illinois Journal of Mathematics

Exponentially bounded positive definite functions

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.

Article information

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

Dates
First available in Project Euclid: 20 October 2009

https://projecteuclid.org/euclid.ijm/1256046160

Digital Object Identifier
doi:10.1215/ijm/1256046160

Mathematical Reviews number (MathSciNet)
MR730718

Zentralblatt MATH identifier
0519.43005

Citation

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