Timeline for Is the space $C_0^{k}(\Omega)$ a Montel space?
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 27 at 21:19 | vote | accept | Math | ||
| Mar 27 at 16:31 | answer | added | Ayman Moussa | timeline score: 1 | |
| Mar 27 at 16:05 | comment | added | Ayman Moussa | Just to be sure : $C^k_0(\Omega)$ is the set of compactly (in $\Omega$) $C^k(\Omega)$ functions that you equip with the inductive limit topology for which $(\varphi_n)_n\rightarrow \varphi$ means existence of $K$ compact subset of $\Omega$ containing supports of all $\varphi_n$ and $\varphi$ function, with uniform convergence on $K$ up to the $k$-th derivative ? | |
| Mar 27 at 15:02 | comment | added | Math | @DieterKadelka Yes, this result is also found in Trèves and Horváth's books. My question is when $0\leq k <\infty$. | |
| Mar 27 at 14:13 | comment | added | Dieter Kadelka | At least for $k = \infty$ $C_0^\infty(\Omega)$ is a Montel space (Bourbaki, Topological Vector Spaces IV, Example 4 on p. IV.18). | |
| Mar 27 at 13:23 | history | asked | Math | CC BY-SA 4.0 |