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Proceedings of the American Mathematical Society

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Fourier transforms and measure-preserving transformations


Author: O. Carruth McGehee
Journal: Proc. Amer. Math. Soc. 44 (1974), 71-77
MSC: Primary 42A68
MathSciNet review: 0338678
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Abstract: There exists a continuous function $ f$ on the real line, vanishing at infinity, such that, for every measure-preserving transformation $ h$, the composition $ f \circ h$ fails to be a Fourier transform. This fact is a consequence of a theorem about measurable functions which is obtained from the theory of idempotents.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1974-0338678-8
Keywords: Fourier transforms, idempotents, measure-preserving transformations
Article copyright: © Copyright 1974 American Mathematical Society