Is there an example of a periodic continuous function on $\mathbb{R}$ such that its Fourier series is uniformly convergent (to $f$), but it is not absolutely convergent ?
2026-04-03 10:03:28.1775210608
Function with uniformly but non absolutely convergent Fourier series
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$\sum \frac {\sin (nx)} {n\log \, n}$ is such a series. The proof is not obvious but it is a well known result. See Edwards, Fourier Series. p. 166.