Timeline for Weak continuity under Laplace transform
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 16, 2019 at 16:57 | vote | accept | Saj_Eda | ||
| Nov 14, 2019 at 21:45 | comment | added | Yuval Peres | The comments are not really designed for asking additional questions. Without further assumptions the converse does not hold, consider $u_n(x)=n/x$ for $x>n$ and $u_n(x)=0$ elsewhere. Then $L(u_n)$ tends to $L(0)=0$ pointwise for $s>0$, but $\int_0^\infty u_n u_1\, dx=1$ for all $n$. | |
| Nov 14, 2019 at 21:38 | comment | added | Yuval Peres | If the above answered your question, you can indicate that by accepting the answer. meta.mathoverflow.net/questions/3724/how-to-accept-answer | |
| Nov 14, 2019 at 16:24 | comment | added | Saj_Eda | Is the converse also true? That is, if $L(u_n)(s)$ converges pointwise to $L(u)(s)$, then $u_n(t)$ converges weakly to $u(t)$? | |
| Nov 14, 2019 at 5:59 | history | answered | Yuval Peres | CC BY-SA 4.0 |