Nihonkai Mathematical Journal

Integral Representations of Positive Definite Functions on Convex Sets of Certain Semigroups of Rational Numbers

Koji Furuta

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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.

Article information

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

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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]

moment problem positive definite function semigroup


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.

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