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

 

The uncertainty principle on Riemannian symmetric spaces of the noncompact type


Author: J. Sengupta
Journal: Proc. Amer. Math. Soc. 130 (2002), 1009-1017
MSC (2000): Primary 43A85, 22E30
Published electronically: August 29, 2001
MathSciNet review: 1873774
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Abstract:

The uncertainty principle in ${\mathcal R}^{n}$ says that it is impossible for a function and its Fourier transform to be simultaneously very rapidly decreasing. A quantitative assertion of this principle is Hardy's theorem. In this article we prove various generalisations of Hardy's theorem for Riemannian symmetric spaces of the noncompact type. In the case of the real line these results were obtained by Morgan and Cowling-Price.


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Additional Information

J. Sengupta
Affiliation: School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay - 400 005, India
Email: sengupta@math.tifr.res.in

DOI: http://dx.doi.org/10.1090/S0002-9939-01-06318-3
PII: S 0002-9939(01)06318-3
Received by editor(s): September 18, 2000
Published electronically: August 29, 2001
Communicated by: Rebecca Herb
Article copyright: © Copyright 2001 American Mathematical Society