Timeline for Decomposing an analytic function into two functions which vanish at $0$ and $\infty?$
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 25, 2021 at 14:16 | comment | added | Wojowu | I don't know what you mean with it, but usually it means "analytic on $\mathbb C$ and analytic at $\infty$". If you allow meromorphic functions, then by the same argument as in the answer there will be no examples on all of $\hat{\mathbb C}$ either. | |
| May 25, 2021 at 14:13 | comment | added | Ma Joad | @Wojowu Doesn't "analytic on Riemann sphere" actually mean "meromorphic on $\mathbb C?$" | |
| May 25, 2021 at 14:04 | comment | added | Wojowu | The only functions analytic on the entire Riemann sphere are constant. | |
| May 25, 2021 at 14:04 | comment | added | Ma Joad | But the focus is - why it exists if $U=\hat {\mathbb C}?$ (If I have explained clearly enough.) | |
| May 25, 2021 at 13:54 | comment | added | Wojowu | This answer implies that such an example can't exist if $U$ is not all of $\hat\mathbb C$. | |
| May 25, 2021 at 13:33 | comment | added | Ma Joad | I am looking for an example where $f$ cannot be written in this form! | |
| May 25, 2021 at 13:29 | history | answered | André Henriques | CC BY-SA 4.0 |