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How to prove that if Fourier series of function $f$ converge uniformly, then function is continuous?

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    If you mean that the Fourier series converges uniformly to $f$, then this simply follows from the fact that a uniform limit of continuous functions is continuous.2012-05-23
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    I'm sorry, Fourier series, not coefficient. If for $f(t)$ exists Fourier series that converge uniformly $\sum_{k\in \mathbb{Z} }{c_k e^{(-2i\pi kt)}}$ on $[0,1]$ then $f(t)$ is continious.2012-05-23
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    @M Turgeon yes i know this theorem, but is this theorem true under $\mathbb{C}$ - functions?2012-05-23
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    @user31919 see my answer below2012-05-23

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