I am a bit confused. I have heard today someone saying that the Fourier series of any continues periodic function $f$, say with period 1 for concreteness, converges pointwise to $f$. Wikipedia here explicitly says otherwise, but claims that the proof is not constructive and somewhat advanced. So what is it?
I have to apologize for this question, since I could just pick any book about Fourier analysis and check it up myself, but since the answer is a simple "yes" or "no" I hope it is not to much of an effort to answer this for someone how knows the answer.