Abstract
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 $\boldsymbol Q^2$.
Acknowledgment
The author would like to express his gratitude to the referee for valuable comments.
Citation
Koji Furuta. "Integral Representations of Positive Definite Functions on Convex Sets of Certain Semigroups of Rational Numbers." Nihonkai Math. J. 28 (2) 79 - 88, 2017.
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