Timeline for Let $u_n\in\mathcal{D}'(\mathbb{R}^n)$ have $u_n\to0$ where $u_n\in C_c^\infty$ have uniformly compact support. Does $u_n\to0$ in $C_c^\infty$?
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
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| Oct 12, 2017 at 22:58 | comment | added | reuns | @MonstrousMoonshine It follows from : if $u$ is a given compactly supported distribution then $|\langle u,\varphi \rangle| \le C \sum_{n \le N} \|D^n \varphi\|_\infty$ for some $N,C$. In general $u \psi$ is compactly supported distribution for any $\psi \in C^\infty_c$ | |
| Oct 12, 2017 at 16:12 | comment | added | Mateusz Kwaśnicki | @MonstrousMoonshine: For example, Vladimirov, Methods of the Theory of Generalized Functions, Section 2.4. | |
| Oct 12, 2017 at 14:19 | comment | added | Dominic Wynter | Could you provide a reference for the fact that any distribution is locally the derivative of a bounded function? | |
| Oct 12, 2017 at 7:45 | history | answered | Mateusz Kwaśnicki | CC BY-SA 3.0 |