Timeline for A maximum of an integral
Current License: CC BY-SA 4.0
15 events
| when toggle format | what | by | license | comment | |
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| Jul 18, 2020 at 12:20 | comment | added | Lira | @Iosif Pinelis... Take $\omega = (z-w)/(1-\bar z w)$. Then the Jacobian is $J= |\frac{1-|z|^2}{\left(-1+\omega\bar{z}\right)^2}|^2 $ and so on... | |
| Jul 17, 2020 at 20:11 | comment | added | Iosif Pinelis | @Lira : Can you detail the use of the Möbius transformation? | |
| Jul 17, 2020 at 16:53 | comment | added | Wolfgang | I think you meant @Iosif. | |
| Jul 17, 2020 at 14:15 | comment | added | Lira | @Wolfgang By using a Mebius trasformation, the second formulation can be transformed to the fist one. | |
| Jul 17, 2020 at 13:14 | comment | added | Wolfgang | @Fedor oh sorry, maybe not... Didn't realize that $\bar z$ rotates the other way round when rotating z! | |
| Jul 16, 2020 at 23:31 | comment | added | Iosif Pinelis | I don't see why the two expressions you give for $G(R,s)$ have the same values. If you write $w=\frac rR\,ze^{ia}$ with $R:=|z|$ and $r:=|w|$, then $|1-\bar zw|^2=1+r^2R^2-2rR\cos a$; but how come the denominator of the expression for $A$ is $(1+r^2R^2-2rR\cos a)^2$? | |
| Jul 16, 2020 at 20:44 | comment | added | Fedor Petrov | @Wolfgang why does it depend only on $|z|$? | |
| Jul 16, 2020 at 20:26 | comment | added | Wolfgang | Written as $\sup_{z\in U}\int_{U}\left|\frac{1}{z-w}-\frac{1}{\bar z -1/w}\right|du dv$, it looks like the integral only depends on |z| and it might just follow from some symmetry considerations that the maximum is attained at z=0. | |
| Jul 16, 2020 at 18:53 | history | edited | Lira | CC BY-SA 4.0 |
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| Jul 16, 2020 at 18:37 | comment | added | Lira | @ Fedor Petrov. Yes, $w=u+iv$. | |
| Jul 16, 2020 at 18:36 | history | edited | Lira | CC BY-SA 4.0 |
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| Jul 16, 2020 at 18:26 | comment | added | Lira | @Fedor Petro: I made some geometric explanation. | |
| Jul 16, 2020 at 18:25 | history | edited | Lira | CC BY-SA 4.0 |
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| Jul 16, 2020 at 18:04 | comment | added | Fedor Petrov | This integral seems to have some geometric meaning. If you have such, would you please share it? | |
| Jul 16, 2020 at 17:59 | history | asked | Lira | CC BY-SA 4.0 |