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Extension and separation properties of positive definite functions on locally compact groups


Authors: Eberhard Kaniuth and Anthony T. Lau
Journal: Trans. Amer. Math. Soc. 359 (2007), 447-463
MSC (2000): Primary 43A35; Secondary 22E25
DOI: https://doi.org/10.1090/S0002-9947-06-03969-9
Published electronically: August 24, 2006
MathSciNet review: 2247899
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Abstract: Continuing earlier work, we investigate two related aspects of the set $ P(G)$ of continuous positive definite functions on a locally compact group $ G$. The first one is the problem of when, for a closed subgroup $ H$ of $ G$, every function in $ P(H)$ extends to some function in $ P(G)$. The second one is the question whether elements in $ G \setminus H$ can be separated from $ H$ by functions in $ P(G)$ which are identically one on $ H$.


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Additional Information

Eberhard Kaniuth
Affiliation: Institut für Mathematik, Universität Paderborn, D-33095 Paderborn, Germany
Email: kaniuth@math.uni-paderborn.de

Anthony T. Lau
Affiliation: Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Canada T6G 2G1
Email: tlau@math.ualberta.ca

DOI: https://doi.org/10.1090/S0002-9947-06-03969-9
Keywords: Locally compact group, positive definite function, extension, separation property, solvable group, almost connected group, SIN-group.
Received by editor(s): June 30, 2004
Received by editor(s) in revised form: February 2, 2005
Published electronically: August 24, 2006
Additional Notes: The second author was supported by NSERC grant A 7679
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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