How to prove that if Fourier series of function $f$ converge uniformly, then function is continuous?
The relationship between Fourier coefficients of function $f$ and its continuity
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functional-analysis
convergence
fourier-series
continuity
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3If 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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0I'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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0@M Turgeon yes i know this theorem, but is this theorem true under $\mathbb{C}$ - functions? – 2012-05-23
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0@user31919 see my answer below – 2012-05-23