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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Minimizing functions for an uncertainty principle on locally compact groups of bounded representation dimension


Author: Eberhard Kaniuth
Journal: Proc. Amer. Math. Soc. 135 (2007), 217-227
MSC (2000): Primary 43A30, 43A40
Published electronically: June 29, 2006
MathSciNet review: 2280190
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Abstract: Let $ G$ be a locally compact group of bounded representation dimension $ d(G)$. Then, for any integrable function $ f$ on $ G$, the product of the measures of the support of $ f$ and the support of its operator-valued Fourier transform on the dual space of $ G$ is bounded below by $ 1/d(G)$. We classify all functions for which equality holds and prove criteria for when such functions exist.


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Additional Information

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

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08451-6
PII: S 0002-9939(06)08451-6
Received by editor(s): July 9, 2005
Received by editor(s) in revised form: August 1, 2005
Published electronically: June 29, 2006
Communicated by: Michael T. Lacey
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.