Extension and separation properties of positive definite functions on locally compact groups
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- by Eberhard Kaniuth and Anthony T. Lau PDF
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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 $H$.References
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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
- MR Author ID: 110640
- Email: tlau@math.ualberta.ca
- 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
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2247899