Where can I find an example (or the theorem) for a continuous function which does not converge pointwise to its Fourier series, as well as its explanation?
I would prefer a web page or a free site or an "easy" to find book.
Thanks for your help!
Asked
Active
Viewed 3,395 times
0
-
Just googling your title brings up this http://math.stackexchange.com/questions/2227/example-of-a-function-whose-fourier-series-fails-to-converge-at-one-point and this http://math.stackexchange.com/questions/442098/function-not-satisfying-pointwise-convergence-and-fourier-series as #3 and #4. – Conifold Jul 17 '14 at 22:14
-
@Conifold I don't see how either of these posts answer the question. They do not contain an example of a continuous function for which the Fourier series fails to converge pointwise. – Jul 17 '14 at 22:39
-
Part of the problem is that "does not converge pointwise" or "fails to converge pointwise" could mean both at every point or at some point. Both links above give examples for the latter, which is simpler. Diverging everywhere isn't hard to google either, here http://math.stackexchange.com/questions/14855/an-example-of-a-continuous-function-whose-fourier-series-diverges-at-a-dense-set. – Conifold Jul 17 '14 at 22:58
-
@Conifold Okay, I did not notice the answer at the bottom of the first-linked question. But the second link in your first comment wouldn't work: there is no continuous function there. – Jul 18 '14 at 04:54