Timeline for Is the endpoint map smooth
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| S Sep 1, 2015 at 19:57 | history | suggested | Benjamin | CC BY-SA 3.0 |
added a missing comma and a missing word
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| Sep 1, 2015 at 19:48 | review | Suggested edits | |||
| S Sep 1, 2015 at 19:57 | |||||
| May 21, 2015 at 8:14 | comment | added | Peter Michor | Its true on every Lie group. Even on diffeomorphism groups. Groups with this property are called regular Lie groups. Look into the references. | |
| May 21, 2015 at 6:26 | comment | added | Benjamin | Great. How special is this property of the end point map being smooth? Am I right in saying that no specific property of $SU(n)$ was used? Or in fact even of the specific differential equation? | |
| May 21, 2015 at 6:17 | comment | added | Peter Michor | A finite dimensional vector space is completely fine. Anything that maps smoothly into $C^\infty(\mathbb R, \mathfrak{su}(n)$ just follows. I might add something on $L^2$ when I have time. You might look into mat.univie.ac.at/~michor/convenient-overview.pdf | |
| May 20, 2015 at 20:16 | comment | added | Benjamin | Also, do you think this would work if the set of $w$ was just some smooth (finite dim) vector space of $C^{\infty}$ functions rather than an infinite dim one. | |
| May 20, 2015 at 20:15 | comment | added | Benjamin | Thanks, that great. Do you mean that it's harder to prove that $V_T$ is smooth in the $L^2([0,T])$ case or that you need to "work hard" in the sense of adding extra assumptions on $w,a,b$. | |
| May 20, 2015 at 18:40 | history | answered | Peter Michor | CC BY-SA 3.0 |