Timeline for Given functions $A(x), B(x)$ find $f(x)$ s.t. $A\big(f(x)\big)=f\big(B(x)\big)$
Current License: CC BY-SA 4.0
17 events
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| Feb 10, 2020 at 14:13 | comment | added | JustaRegularSchroedinger | Alexandre, I was checking if I could add some extra assumptions which are not too stringent. Assuming they all are continuous is acceptable. Regarding f, we can also assume it to be derivable. | |
| Feb 10, 2020 at 13:12 | comment | added | Laurent Berger | Also, does this type of problem have a specific name? Given two maps $A$ and $B$, trying to find an $f$ such that $A \circ f =f \circ B$ is a problem of semi-conjugacy. | |
| Feb 10, 2020 at 13:10 | comment | added | YCor | More formally one can write the equation as $A\circ\vec{f}=f\circ B$, where $\vec{f}=f^{\times n}$. | |
| Feb 10, 2020 at 13:10 | comment | added | Alexandre Eremenko | Are your functions supposed to be continuous? | |
| Feb 10, 2020 at 13:09 | answer | added | Alexandre Eremenko | timeline score: 5 | |
| Feb 10, 2020 at 13:00 | history | edited | YCor |
edited tags
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| S Feb 10, 2020 at 12:41 | history | edited | David White | CC BY-SA 4.0 |
Minor Math Jaxing. This edit does not add much to the post, so feel free to naot approve it
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| S Feb 10, 2020 at 12:41 | history | suggested | Daniele Tampieri | CC BY-SA 4.0 |
Minor Math Jaxing. This edit does not add much to the post, so feel free to naot approve it
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| Feb 10, 2020 at 11:04 | review | Suggested edits | |||
| S Feb 10, 2020 at 12:41 | |||||
| Feb 10, 2020 at 10:27 | comment | added | JustaRegularSchroedinger | Thanks for answering, Yaakov! Regarding the assumptions, I am looking to see under which conditions f exists and when it doesn't. In your example, we saw that f doesn't exist, however, there are cases in which it does. E.g. $$ A( \vec x ) = \prod x_i$$ $$ B( \vec x ) = \sum x_i$$ In this case the solution is: $$ f( x ) = e^x $$ So, I am looking to see if there are certain conditions under which f exists (and eventually how to find it). I'll be happy also just to know if there is a class of similar problems and their name. | |
| Feb 10, 2020 at 10:09 | comment | added | Yaakov Baruch | It seems too easy: if $A(x_1,x_2)=1+x_1$ and $B(x_1,x_2)=x_1+x_2$ then you are looking for $f$ such that $1+f(x_1)=f(x_1+x_2)$ which cannot be, for example if $x_2=0$. Maybe you missed some conditions? (Or did I?) | |
| Feb 10, 2020 at 9:58 | comment | added | JustaRegularSchroedinger | Ok, I also changed the nick to a more appropriate one. I guess the next answer I'll receive is not gonna be on the question I asked, but on the way, I use the comma. Maybe I should ask this same question on a grammar forum... | |
| Feb 10, 2020 at 9:49 | comment | added | Carlo Beenakker | you might also want to consider changing the name of your profile; the adjectives you use to characterise Schrödinger are inappropriate, IMO. | |
| Feb 10, 2020 at 9:37 | comment | added | JustaRegularSchroedinger | Fixed! I hope now it's fun enough | |
| Feb 10, 2020 at 9:36 | history | edited | JustaRegularSchroedinger | CC BY-SA 4.0 |
deleted 1 character in body
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| Feb 10, 2020 at 9:10 | review | First posts | |||
| Feb 10, 2020 at 9:20 | |||||
| Feb 10, 2020 at 9:08 | history | asked | JustaRegularSchroedinger | CC BY-SA 4.0 |