Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Hardy's theorem
for the $n$-dimensional Euclidean motion group


Author: M. Sundari
Journal: Proc. Amer. Math. Soc. 126 (1998), 1199-1204
MSC (1991): Primary 22Exx; Secondary 22E30, 43A80
MathSciNet review: 1423336
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Abstract: An uncertainty principle, due to Hardy, for Fourier transform pairs on $\Bbb R$ says that if the function $f$ is ``very rapidly decreasing'', then the Fourier transform cannot also be ``very rapidly decreasing'' unless $f$ is identically zero. In this paper we state and prove an analogue of Hardy's theorem for the $n$-dimensional Euclidean motion group.


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Additional Information

M. Sundari
Affiliation: Statistics and Mathematics Division, Indian Statistical Institute, 8th Mile, Mysore Road, R V College Post Office, Bangalore - 560 059, India
Email: sundari@isibang.ernet.in

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04144-6
Keywords: Uncertainty principle, Fourier transform pairs, very rapidly decreasing, Euclidean motion group
Received by editor(s): April 4, 1995
Received by editor(s) in revised form: September 3, 1996
Communicated by: J. Marshall Ash
Article copyright: © Copyright 1998 American Mathematical Society