[Merged by Bors] - feat(analysis/fourier): convergence of Fourier series #17913
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Co-authored-by: sgouezel <sebastien.gouezel@univ-rennes1.fr>
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Speed up all 30 declaration with elaboration time > 10s (on my machine).
…o jyxu/identify_interval_ends2
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Marking this as draft because in the time it took for the prerequisites to get merged, I realised that the changes to "continuous_map.eval_clm" could be done in a different (bettter) way. |
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... and the alternative approach doesn't work. Sorry for the noise. |
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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`.) Co-authored-by: Junyan Xu <junyanxu.math@gmail.com>
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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 offis absolutely summable, then the Fourier series converges uniformly, and hence pointwise everywhere, tof. (Note that it is obvious in this case that the Fourier series converges uniformly to something, the difficult part is that the limit is actuallyf.)homeo_Icc_quotfrom ℝ to archimedean groups #17983