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Proceedings of the American Mathematical Society

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

 
 

 

The Fourier transform is onto only when the group is finite


Author: Stephen H. Friedberg
Journal: Proc. Amer. Math. Soc. 27 (1971), 421-422
MSC: Primary 43A25
DOI: https://doi.org/10.1090/S0002-9939-1971-0412736-9
MathSciNet review: 0412736
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Abstract: A well-known result of Henry Helson is used to prove that a locally compact abelian group is finite if and only if the Fourier transform is a surjective map.


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DOI: https://doi.org/10.1090/S0002-9939-1971-0412736-9
Keywords: Locally compact abelian group, dual group, Fourier transform, extremally disconnected, Helson set, Haar measure, Tietze Extension Theorem
Article copyright: © Copyright 1971 American Mathematical Society

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