Timeline for Bounding a series of nested integrals
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 25, 2018 at 13:36 | comment | added | user539887 | @lcv You're right, that's the same. I removed my comment. | |
| May 25, 2018 at 8:55 | comment | added | lcv | @user539887 the Peano-Baker series is precisely the OP’s series. Or did you have something else in mind? | |
| May 25, 2018 at 3:38 | comment | added | lcv | Is $f(t)$ anti-hermitian? That would help | |
| May 24, 2018 at 20:41 | comment | added | user539887 | No, I don't know exactly: just thinking aloud. | |
| May 24, 2018 at 20:32 | comment | added | Ludwig | So, do you mean that, from the fact $\|e^{tS}\|=1$, a bound on (the norm of) the Magnus expansion can be found? (I don't see how...) | |
| May 24, 2018 at 20:22 | comment | added | user539887 | Yes, for any $x \in \mathbb{R}^n$ there holds $\langle e^{tS}x, e^{tS}x \rangle' = \langle Se^{tS}x, e^{tS}x \rangle + \langle e^{tS}x, Se^{tS}x \rangle = \langle e^{tS}x, (S - S) e^{tS}x \rangle = 0$, that is, $\lVert e^{tS} \rVert = 1$ for all $t \in \mathbb{R}$. | |
| May 24, 2018 at 16:57 | comment | added | Ludwig | Thanks for your input! Suppose that $[A_1,A_2]=S$, where $S$ is skew-symmetric (here square brackets denote commutator). Do you think this assumption could be helpful? | |
| May 23, 2018 at 9:20 | history | answered | user539887 | CC BY-SA 4.0 |