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The representation of functions (or objects which are in some generalize the notion of function) as constant linear combinations of sines and cosines at integer multiples of a given frequency, as Fourier transforms or as Fourier integrals.

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A Fourier series that does not converge in $L^1$

I'm reading Katznelson's book "Harmonic Analysis" and there is an exercise that I can't solve : Show that if the sequence $\left\{ N_j \right\} $ tends to infinity fast enough, then the Fourier …
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