Positive Semicharacters of Lie Semigroups

Positive Semicharacters of Lie Semigroups We study positive semicharacters of generating Lie subsemigroup $$S$$ of a connected Lie group $$G$$ . These semicharacters are important for positive representations of $$S$$ in Hilbert space and for completely monotonic functions in $$S$$ . We describe the tangent map for a positive semicharacter and then obtain a necessary and sufficient condition for nontriviality of the wedge $$S_1^*$$ consisting of all bounded positive semicharacters of $$S$$ . In particular $$S_1^*$$ is nontrivial for a solvable simply connected $$G$$ and invariant $$S$$ without nontrivial subgroups, but it is trivial for a semisimple $$G$$ . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

Positive Semicharacters of Lie Semigroups

Positivity , Volume 3 (1) – Oct 22, 2004

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Publisher
Springer Journals
Copyright
Copyright © 1999 by Kluwer Academic Publishers
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1023/A:1009703125617
Publisher site
See Article on Publisher Site

Abstract

We study positive semicharacters of generating Lie subsemigroup $$S$$ of a connected Lie group $$G$$ . These semicharacters are important for positive representations of $$S$$ in Hilbert space and for completely monotonic functions in $$S$$ . We describe the tangent map for a positive semicharacter and then obtain a necessary and sufficient condition for nontriviality of the wedge $$S_1^*$$ consisting of all bounded positive semicharacters of $$S$$ . In particular $$S_1^*$$ is nontrivial for a solvable simply connected $$G$$ and invariant $$S$$ without nontrivial subgroups, but it is trivial for a semisimple $$G$$ .

Journal

PositivitySpringer Journals

Published: Oct 22, 2004

References

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