Timeline for Sets of divergence of Fourier series
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 7, 2011 at 2:59 | comment | added | Robert Israel | In the problem as stated, the series "diverges at all points of $E$ and pointwise converges to $f$ at all points not in $E$". So $E^c$ is the whole set of convergence. | |
| Jun 7, 2011 at 1:28 | comment | added | Zen Harper | ...Of course, for continuous $f$ at least. | |
| Jun 7, 2011 at 1:28 | comment | added | Zen Harper | Andres: I think it's the whole set of convergence: if $f$ is continuous at a point $x$ and $S_n(f)(x)$ has some limit, then the limit must be $f(x)$, because of Fejer's Theorem: the Cesaro means $\sigma_n(f)(x)$ always converge to $f(x)$ at points of continuity, and Cesaro means preserve limits. | |
| Jun 7, 2011 at 1:15 | comment | added | Andrés E. Caicedo | Yes, Robert. I added a link in the body of the question to a problem where this is used. Note here that we want convergence to $f(x)$, so we are taking a subset of the set of convergence. | |
| Jun 7, 2011 at 1:10 | history | answered | Robert Israel | CC BY-SA 3.0 |