The Fourier transform is onto only when the group is finite
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- by Stephen H. Friedberg PDF
- Proc. Amer. Math. Soc. 27 (1971), 421-422 Request permission
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.References
- Raouf Doss, Elementary proof of a theorem of Helson, Proc. Amer. Math. Soc. 27 (1971), 418–420. MR 271644, DOI 10.1090/S0002-9939-1971-0271644-7
- M. Rajagopalan, Fourier transform in locally compact groups, Acta Sci. Math. (Szeged) 25 (1964), 86–89. MR 168995
- Walter Rudin, Fourier analysis on groups, Interscience Tracts in Pure and Applied Mathematics, No. 12, Interscience Publishers (a division of John Wiley & Sons, Inc.), New York-London, 1962. MR 0152834
- I. E. Segal, The class of functions which are absolutely convergent Fourier transforms, Acta Sci. Math. (Szeged) 12 (1950), 157–161. MR 36943
Additional Information
- © Copyright 1971 American Mathematical Society
- 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