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

 

$L^p$ version of Hardy's theorem on semisimple Lie groups


Authors: E. K. Narayanan and S. K. Ray
Journal: Proc. Amer. Math. Soc. 130 (2002), 1859-1866
MSC (2000): Primary 22E30; Secondary 22E46, 43A30
Published electronically: January 16, 2002
MathSciNet review: 1887035
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Abstract: We prove an analogue of the $L^p$ version of Hardy's theorem on semisimple Lie groups. The theorem says that on a semisimple Lie group, a function and its Fourier transform cannot decay very rapidly on an average.


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Additional Information

E. K. Narayanan
Affiliation: Stat-Math Unit, Indian Statistical Institute, 8th Mile Mysore Road, Bangalore 560 059, India
Address at time of publication: Department of Mathematics & Computer Sciences, Bar-Ilan University, 52900 Ramat-Gan, Israel
Email: naru@isibang.ac.in, naru@macs.biu.ac.il

S. K. Ray
Affiliation: Stat-Math Unit, Indian Statistical Institute, 203 B. T. Road, Calcutta 700035, India
Address at time of publication: Department of Mathematics, Indian Institute of Technology, Kanpur, U.P.-208016, India
Email: res9601@www.isical.ac.in, skray@iitk.ac.in

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06272-X
PII: S 0002-9939(02)06272-X
Keywords: Hardy's theorem, uncertainty principle, semisimple Lie groups
Received by editor(s): July 25, 2000
Received by editor(s) in revised form: January 2, 2001
Published electronically: January 16, 2002
Additional Notes: This research was supported by NBHM, India
Communicated by: Christopher D. Sogge
Article copyright: © Copyright 2002 American Mathematical Society