Fourier transforms and measure-preserving transformations

McGehee, O. Carruth

doi:10.1090/S0002-9939-1974-0338678-8

Fourier transforms and measure-preserving transformations
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Proc. Amer. Math. Soc. 44 (1974), 71-77 Request permission

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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