Nihonkai Mathematical Journal
- Nihonkai Math. J.
- Volume 28, Number 2 (2017), 79-88.
Integral Representations of Positive Definite Functions on Convex Sets of Certain Semigroups of Rational Numbers
H. Glöckner proved that an operator-valued positive definite function on an open convex subset of $\boldsymbol Q^N$ is a restriction of the Laplace transform of an operator-valued measure on $\boldsymbol R^N$. We generalize this result to a function on an open convex subset of a certain subsemigroup of $\boldsymbol Q^2$.
The author would like to express his gratitude to the referee for valuable comments.
Nihonkai Math. J., Volume 28, Number 2 (2017), 79-88.
Received: 2 May 2016
Revised: 7 June 2017
First available in Project Euclid: 26 April 2018
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 43A35: Positive definite functions on groups, semigroups, etc.
Secondary: 44A60: Moment problems 47A57: Operator methods in interpolation, moment and extension problems [See also 30E05, 42A70, 42A82, 44A60]
Furuta, Koji. Integral Representations of Positive Definite Functions on Convex Sets of Certain Semigroups of Rational Numbers. Nihonkai Math. J. 28 (2017), no. 2, 79--88. https://projecteuclid.org/euclid.nihmj/1524708082