Commit 2023-01-08 13:02 247a102b
View on Github →feat(analysis/fourier): convergence of Fourier series (#17913)
This PR adds a straightforward but useful criterion for convergence of Fourier series: for a continuous periodic function f
, if the sequence of Fourier coefficients of f
is absolutely summable, then the Fourier series converges uniformly, and hence pointwise everywhere, to f
. (Note that it is obvious in this case that the Fourier series converges uniformly to something, the difficult part is that the limit is actually f
.)