A Characterization of Fourier Transforms
نویسنده
چکیده
The aim of this paper is to show that, in various situations, the only continuous linear map that transforms a convolution product into a pointwise product is a Fourier transform. We focus on the cyclic groups Z/nZ, the integers Z, the Torus T and the real line. We also ask a related question for the twisted convolution. In memory of A. Hulanicki.
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