Hardy’s theorem for the $n$-dimensional Euclidean motion group
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- by M. Sundari PDF
- Proc. Amer. Math. Soc. 126 (1998), 1199-1204 Request permission
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
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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
- Received by editor(s): April 4, 1995
- Received by editor(s) in revised form: September 3, 1996
- Communicated by: J. Marshall Ash
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 126 (1998), 1199-1204
- MSC (1991): Primary 22Exx; Secondary 22E30, 43A80
- DOI: https://doi.org/10.1090/S0002-9939-98-04144-6
- MathSciNet review: 1423336