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Proceedings of the American Mathematical Society

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The Fourier transform is onto only when the group is finite


Author: Colin C. Graham
Journal: Proc. Amer. Math. Soc. 38 (1973), 365-366
MSC: Primary 43A25
DOI: https://doi.org/10.1090/S0002-9939-1973-0313716-6
MathSciNet review: 0313716
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Abstract: A very simple proof of the result of the title is given. Unlike previous proofs, the one presented here uses no results of harmonic analysis beyond the Pontryagin duality theorem.


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

  • [1] S. H. Friedberg, The Fourier transform is onto only when the group is finite, Proc. Amer. Math. Soc. 27 (1971), 421-422. MR 0412736 (54:857)
  • [2] M. Rajagopalan, Fourier transform in locally compact groups, Acta Sci. Math. (Szeged) 25 (1964), 86-89. MR 29 #6250. MR 0168995 (29:6250)
  • [3] I. E. Segal, The class of functions which are absolutely convergent Fourier transforms, Acta Sci. Math. (Szeged) 12 (1950), Pars B, 157-161. MR 12, 188; 1002. MR 0036943 (12:188d)
  • [4] G. Rabson, The existence of nonabsolutely convergent Fourier series on compact groups, Proc. Amer. Math. Soc. 10 (1959), 893-897. MR 22 #2910. MR 0112052 (22:2910)

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DOI: https://doi.org/10.1090/S0002-9939-1973-0313716-6
Article copyright: © Copyright 1973 American Mathematical Society

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