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$f$ continuous in $R$ with period $2\pi$ and

$f(t) = \sum_{k=- \infty }^{\infty} c_{k} e^{ikt} $

where $c_{k}$ is the complex Fourier coefficient of $f$ then

$\lim_{k \rightarrow \infty} |c_{k}|=0$

Is this true or false? If it's true can someone point me in the right direction on how to proof it? If it's false can someone give a counter example?

Thanks in advance!

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Thanks ! This lemma is not mentioned in my syllabus thank you for giving me this link. – tim_a Jan 25 '13 at 10:31

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