Please give me a link to a reference for an example of a continuous function whose Fourier series diverges at a dense set of points. (given by Du Bois-Reymond). I couldn't find this in Wikipedia.
Fourier Series – Example of a Continuous Function Whose Fourier Series Diverges at a Dense Set of Points
fourier seriesreference-request
Best Answer
As I mentioned in comments below, Kolmogorov's example is for a discontinuous function in $L^1$.
For a continuous function whose Fourier series diverges at all rational multiples of $2\pi$ (and hence on a dense set) see Katznelson's book: An Introduction to Harmonic Analysis Chapter 2, Remark after proof of Theorem 2.1. Note that the Fourier series of such a continuous function still converges almost everywhere by Carleson's theorem.