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

 

An analogue of Hardy's theorem for semi-simple Lie groups


Author: J. Sengupta
Journal: Proc. Amer. Math. Soc. 128 (2000), 2493-2499
MSC (1991): Primary 22E30; Secondary 22E46, 43A30
Published electronically: February 25, 2000
MathSciNet review: 1654100
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Abstract:

A well known theorem of Hardy on Fourier transform pairs says that a function $f$ on ${\mathbf R}^n$ and its Fourier transform $\stackrel{\wedge}{f}$ cannot both be ``very rapidly decreasing''. We prove here an analogue of this result in the case of semi-simple Lie groups.


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Additional Information

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

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05258-8
PII: S 0002-9939(00)05258-8
Received by editor(s): July 16, 1998
Received by editor(s) in revised form: September 16, 1998
Published electronically: February 25, 2000
Communicated by: Roe Goodman
Article copyright: © Copyright 2000 American Mathematical Society