= Fourier transform of a finite measure
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{title2=$\widehat\mu(\xi)=\int e^{-ix\cdot\xi}\,d\mu(x)$}
The angular-frequency <Fourier transform> of a <finite measure>, or a complex measure of finite total variation, is defined by the displayed integral. It is bounded by total variation and continuous by <dominated convergence>. An integrable density recovers the ordinary <Fourier transform> of a function. A measure supported on a curved surface instead leads to a <Fourier extension operator>.
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