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Variations on a theorem of Cowling and Price with applications to nilpotent Lie groups

Part of: Abstract harmonic analysis

Published online by Cambridge University Press:  09 April 2009

S. Parui  and
S. Thangavelu
S. Parui
Affiliation:
Stat.-Math. Division Indian Statistical Institute203 B.T. Road Kolkata 700108India e-mail: [email protected]
S. Thangavelu
Affiliation:
Department of Mathematics Indian Institute of ScienceBangalore 560012India e-mail: [email protected]
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Abstract

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In this paper we prove a new version of the Cowling-Price theorem for Fourier transforms on Rn. Using this we formulate and prove an uncertainty principle for operators. This leads to an analogue of the Cowling-Price theorem for nilpotent Lie groups. We also prove an exact analogue of the Cowling-Price theorem for the Heisenberg group.

Keywords

Weyl transformnilpotent Lie groupsheat kernelHermite and special Hermite functions.

MSC classification

Secondary: 43A30: Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc.
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 82 , Issue 1 , February 2007 , pp. 11 - 27
Copyright
Copyright © Australian Mathematical Society 2007

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