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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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.
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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