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Convergence of series, sequences and functions and different modes of convergence.

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Are there examples of functions in $L_1$ and $L_\infty$ whose Fourier series divergent ("wea...

It is wellknown that there is a convergence in norm for Fourier series in $L_p$, if $1<p<\infty$, but are there some examples for pointwise divergence if $p=1,\infty$ in books, or somewhere? I have on …
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