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Paley–Wiener theorem

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Paley–Wiener theorem

any of a family of theorems relating decay properties of a function or distribution at infinity with analyticity of its Fourier transform

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About Paley–Wiener theorem

In mathematics, a Paley–Wiener theorem is a theorem that relates decay properties of a function or distribution at infinity with analyticity of its Fourier transform. It is named after Raymond Paley (1907–1933) and Norbert Wiener (1894–1964) who, in 1934, introduced various versions of the theorem. The original theorems did not use the language of distributions, and instead applied to square-integrable functions. The first such theorem using distributions was due to Laurent Schwartz. These theorems heavily rely on the triangle inequality.

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