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Uncertainty principles like Hardy's theorem on some Lie groups

Part of: Lie groups

Published online by Cambridge University Press:  09 April 2009

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

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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.

Keywords

Uncertainty principlesHeisenberg groupsEuclidean motion groupOscillator groupHardy's theorem

MSC classification

Secondary: 22E25: Nilpotent and solvable Lie groups 22E30: Analysis on real and complex Lie groups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 65 , Issue 3 , December 1998 , pp. 289 - 302
Copyright
Copyright © Australian Mathematical Society 1998

References

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