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

J. Aust. Math. Soc. 82 (2007), 11-27

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

S. Parui
Stat.-Math. Division
Indian Statistical Institute
203 B.T. Road
Kolkata 700108
India
sanjuparui@gmai.com

and

S. Thangavelu
Department of Mathematics
Indian Institute of Science
Bangalore 560012
India
veluma@math.iisc.ernet.in

Abstract

In this paper we prove a new version of the Cowling-Price theorem for Fourier transforms on $\mathbb{R}^n$ . 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.

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