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Hardy's theorem for the  -dimensional Euclidean motion group
Author(s):
M.
Sundari
Journal:
Proc. Amer. Math. Soc.
126
(1998),
1199-1204.
MSC (1991):
Primary 22Exx;
Secondary 22E30, 43A80
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Abstract:
An uncertainty principle, due to Hardy, for Fourier transform pairs on  says that if the function  is ``very rapidly decreasing'', then the Fourier transform cannot also be ``very rapidly decreasing'' unless  is identically zero. In this paper we state and prove an analogue of Hardy's theorem for the  -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:
10.1090/S0002-9939-98-04144-6
PII:
S 0002-9939(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
Copyright of article:
Copyright
1998,
American Mathematical Society
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