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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Extension and separation properties of positive definite functions on locally compact groups
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by Eberhard Kaniuth and Anthony T. Lau PDF
Trans. Amer. Math. Soc. 359 (2007), 447-463 Request permission

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
  • 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