article are those of harmonic analysis, such that the Fourier transform is both unitary on and an algebra homomorphism from to , without renormalizing the Lebesgue measure.

Background

History

In 1822, Fourier claimed (see ') that any function, whether continuous or discontinuous, can be expanded into a series of sines. That important work was corrected and expanded upon by others to provide the foundation for the various forms

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