Source: cirosantilli/fourier-basis-is-complete-for-l2

= Fourier basis is complete for $\LTwo$
{c}
{id=fourier-basis-is-complete-for-l2}

https://math.stackexchange.com/questions/316235/proving-that-the-fourier-basis-is-complete-for-cr-2-pi-c-with-l2-norm

<Riesz-Fischer theorem> is a norm version of it, and <Carleson's theorem> is stronger pointwise almost everywhere version.

Note that the <Riesz-Fischer theorem> is weaker because the pointwise limit could not exist just according to it: <lp norm sequence convergence does not imply pointwise convergence>.

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