Uncertainty principles like Hardy's theorem on some Lie groups

S. C. Bagchi
and
Swagato K. Ray
Stat-Math Division
Indian Statistical Institute
203, B. T. Road, Calcutta 700 035, India
e-mail: somesh@isical.ac.in & res9601@isical.ac.in

Abstract:

We extend an uncertainty principle due to Cowling and Price to Euclidean spaces, Heisenberg groups and the Euclidean motion group of the plane. This uncertainty principle is a generalisation of a classical result due to Hardy. We also show that on the real line this uncertainty principle is almost equivalent to Hardy's theorem.

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