The Fourier transform is onto only when the group is finite
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- by Colin C. Graham PDF
- Proc. Amer. Math. Soc. 38 (1973), 365-366 Request permission
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
- Stephen H. Friedberg, The Fourier transform is onto only when the group is finite, Proc. Amer. Math. Soc. 27 (1971), 421–422. MR 412736, DOI 10.1090/S0002-9939-1971-0412736-9
- M. Rajagopalan, Fourier transform in locally compact groups, Acta Sci. Math. (Szeged) 25 (1964), 86–89. MR 168995
- I. E. Segal, The class of functions which are absolutely convergent Fourier transforms, Acta Sci. Math. (Szeged) 12 (1950), 157–161. MR 36943
- Gustave Rabson, The existence of nonabsolutely convergent Fourier series on compact groups, Proc. Amer. Math. Soc. 10 (1959), 893–897. MR 112052, DOI 10.1090/S0002-9939-1959-0112052-3
Additional Information
- © Copyright 1973 American Mathematical Society
- 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