Timeline for Oscillation of monotone real-analytic function
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 20 at 11:43 | vote | accept | Severin Schraven | ||
| Oct 20 at 7:17 | history | became hot network question | |||
| Oct 20 at 1:13 | answer | added | Iosif Pinelis | timeline score: 9 | |
| Oct 20 at 1:07 | comment | added | Aleksei Kulikov | I'm not sure so don't quote me on that, but I think Carleman theorem is true even for entire functions? That is, you can even construct such an entire function. To get some positive results you need to impose some growth restriction on the whole of $\mathbb{C}$, then you can get something. | |
| Oct 20 at 0:24 | comment | added | Severin Schraven | @AlekseiKulikov Absolutely, it just goes against all what I believed about real-analytic function. They are nothing like their complex-analytic siblings :( | |
| Oct 20 at 0:22 | comment | added | Aleksei Kulikov | Yes, this one. It seems to answer your question (and any question of this sort) in the negative, but I'm too lazy to work out the details. | |
| Oct 20 at 0:11 | comment | added | Severin Schraven | @AlekseiKulikov Thanks, you seem to refer to something like this math.stackexchange.com/questions/2561363/…. I'll check the Carleman paper, this seems to be an incredibly strong statement. | |
| Oct 19 at 23:49 | comment | added | Aleksei Kulikov | I seem to remember seeing a theorem saying that for any two continuous functions $g_1 < g_2$ there exists a real-analytic function $g$ with $g_1 < g < g_2$, then we can put $f = \int g$, if $g_1$ is positive it will be monotone and $\int g_1 \le \int g \le \int g_2$, and for these integrals it is not too hard to cook up the explosion you need. | |
| Oct 19 at 23:13 | history | asked | Severin Schraven | CC BY-SA 4.0 |