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 $C_c^\infty$? [closed]

11 events

when toggle format	what		by	license	comment
Oct 12, 2017 at 23:46	history	closed	Denis Serre Michael Renardy Sebastian Goette Christian Remling Henry.L		Not suitable for this site
Oct 12, 2017 at 14:55	answer	added	Ayman Moussa		timeline score: 1
Oct 12, 2017 at 13:09	comment	added	Abdelmalek Abdesselam		Try to use the Horvath seminorms as in mathoverflow.net/questions/234025/…
Oct 12, 2017 at 10:05	review	Close votes
Oct 12, 2017 at 23:46
Oct 12, 2017 at 7:45	answer	added	Mateusz Kwaśnicki		timeline score: 1
Oct 12, 2017 at 5:28	answer	added	saone		timeline score: 3
Oct 12, 2017 at 2:20	comment	added	Nate Eldredge		At the level of abstract nonsense, I think there ought to be an argument from the closed graph theorem (the spaces $C^\infty_c(B)$ are Frechet). But in such cases there is often a simple direct argument also.
Oct 12, 2017 at 2:04	comment	added	Dominic Wynter		I see. Then how can we deduce that $$\phi\mapsto u*\phi$$ is continuous?
Oct 12, 2017 at 2:03	comment	added	John Pardon		Definitely not: $\varphi(x)\sin(Nx)\to 0$ in $\mathcal D'(\mathbb R)$ as $N\to\infty$ for any compactly supported smooth function $\varphi$.
Oct 12, 2017 at 1:47	history	edited	Dominic Wynter	CC BY-SA 3.0	added 532 characters in body
Oct 12, 2017 at 1:37	history	asked	Dominic Wynter	CC BY-SA 3.0