A characterization of the Fourier transform and related topics

It is shown that the Fourier transform is essentially, up to a simple adjustment, the only transform on the corresponding space which maps convolutions to products and products to convolutions (surprisingly, no linearity is assumed a priori). To cite this article: S. Alesker et al., C. R. Acad. Sci. Paris, Ser. I 346 (2008).