Timeline for Smoothing operator raising the smoothness exactly by one
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 4, 2015 at 19:45 | answer | added | Anton Petrunin | timeline score: 2 | |
| Apr 4, 2015 at 15:47 | comment | added | Anton Petrunin | @IgorBelegradek, obviously I meant $$\varepsilon\cdot\int\limits_0^x(f(t)-\bar f)\cdot dt.$$ | |
| Apr 4, 2015 at 11:59 | comment | added | Igor Belegradek | @AntonPetrunin: is your approximation of $f$ a $C^\infty$ function plus a constant? If so, the approximation is also $C^\infty$ regardless of $f$. Also is $\bar f=\frac{1}{2\pi}\int f$? | |
| Apr 4, 2015 at 9:22 | comment | added | Liviu Nicolaescu | If the manifold $M$ is non-compact things can get hairy. | |
| Apr 4, 2015 at 2:21 | comment | added | Anton Petrunin | For $M=\mathbb S^1$ one can take $C^\infty$-smoothing and add $\varepsilon\cdot\int (f(x)-\bar f)\cdot dx$, where $\bar f$ is the average value of $f$. | |
| Apr 4, 2015 at 1:18 | history | asked | Igor Belegradek | CC BY-SA 3.0 |