Timeline for Bounding the absolute value of a complex integral
Current License: CC BY-SA 4.0
8 events
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| Jun 2, 2020 at 15:17 | comment | added | seaver | @AlexM. I believe that is kind-of what I want indeed. I have no background in measure theory, so formulating the problem within this field is not my strongest point. The goal would be that with some (structural) knowledge, you can prove this implication. [regarding your edit]: that is unfortunate... :P I am hoping for some luck | |
| Jun 2, 2020 at 15:06 | comment | added | Alex M. | @seaver: I believe that the many concrete details stand in the way of understanding your problem. If $(X,m)$ is a measure space, it seems that you want conditions on $f_1$ and $f_2$ such that $|f_1| \le |f_2|$ should imply $| \int_X f_1 \ \mathrm d m | \le | \int_X f_2 \ \mathrm d m |$. I doubt that you will get anything useful (i.e. anything other than trivial conditions). | |
| Jun 2, 2020 at 14:56 | review | Close votes | |||
| Jun 2, 2020 at 21:15 | |||||
| Jun 2, 2020 at 14:50 | comment | added | seaver | @AlexandreEremenko I think than my question would be, how should I formulate these assumptions on the functions. I'm working on quite a fundamental topic, so having these assumptions to start with is already quite a win :P | |
| Jun 2, 2020 at 14:46 | history | edited | seaver | CC BY-SA 4.0 |
added 328 characters in body
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| Jun 2, 2020 at 14:33 | comment | added | Alexandre Eremenko | This is not true without some additional assumptions on your functions. | |
| Jun 2, 2020 at 14:27 | comment | added | Brendan McKay | I think you need to provide more information about $g_1$ and $g_2$ for this to have a chance. If $g_1$ changes sign a lot and $g_2$ doesn't, the first integral could easily be 0 for some $\omega$ while the second is never 0. | |
| Jun 2, 2020 at 14:11 | history | asked | seaver | CC BY-SA 4.0 |