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- Jun 20, 2014

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Let $f : \Bbb S^1\subset \Bbb C \to \Bbb C$ be a continuous map. Show that if $f$ is continuously differentiable on $\Bbb S^1$, then its Fourier coefficient sequence $\{\hat{f}_n\}_{n\in \Bbb Z}$ belongs to $\ell^1(\Bbb Z)$.

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