Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 22Exx, 22E30, 43A80

Retrieve articles in all journals with MSC (1991): 22Exx, 22E30, 43A80


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
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
Article copyright: © Copyright 1998 American Mathematical Society