Timeline for How can discrete Fourier transform approximation prove the completeness of complex exponentials in $L^2(T)$?

9 events

when toggle format	what		by	license	comment
Aug 19 at 14:10	comment	added	Alexei Entin		Actually I think I can make the argument work, see my answer.
Aug 19 at 13:01	comment	added	Alexei Entin		It seems to me that the ability to reduce to the discrete case depends on the error term $\int_0^1f(x)e^{-2\pi i nx}\mathrm dx-\sum_{k=0}^{N-1}f(k/N)e^{-2\pi ink/N}$. The generic bounds for approximating integrals by Riemann sums give something like $O(n^p/N^p)$ (where $f\in C^p$) which is not good enough.
Aug 19 at 13:00	comment	added	LSpice		MSE's Matt E is our own @Emerton, and you can find contact information on the web page linked in the MO profile.
Aug 19 at 12:59	history	edited	LSpice	CC BY-SA 4.0	Fejer -> Fejér
Aug 19 at 10:21	answer	added	Alexei Entin		timeline score: 1
Aug 18 at 14:07	review	Close votes
Aug 23 at 3:02
Aug 18 at 7:39	history	edited	YCor	CC BY-SA 4.0	removed capitals from title
Aug 18 at 6:59	history	edited	Zhang Yuhan	CC BY-SA 4.0	added 2 characters in body
Aug 18 at 6:47	history	asked	Zhang Yuhan	CC BY-SA 4.0