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I seek a function whose Fourier series is divergent in every point. Thank you very much.

docmat
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    A function in which space? You cannot have an everywhere-divergent Fourier series for a $L^2$ function, for instance. This question - https://math.stackexchange.com/questions/14855/an-example-of-a-continuous-function-whose-fourier-series-diverges-at-a-dense-set - is deeply related. – Jack D'Aurizio Jul 13 '17 at 18:12

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