 Paley–Wiener–Schwartz theorem (source code)

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= Paley–Wiener–Schwartz theorem
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{wiki=Paley–Wiener_theorem}

The Fourier transform of a distribution supported in a compact set $K$ extends to an entire function bounded by a polynomial times $e^{H_K(\operatorname{Im}z)}$, where $H_K$ is the supporting function of $K$. Conversely, every entire function with such a bound is the Fourier--Laplace transform of a distribution supported in $K$.

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