Timeline for Real part of entire function property
Current License: CC BY-SA 4.0
14 events
| when toggle format | what | by | license | comment | |
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| Dec 26, 2019 at 16:39 | comment | added | Alexandre Eremenko | @Guest: a priori this is not clear. I DEFINED $v=\Re(f(z))-\Re(f(\bar{z})$. Only in the end, as a consequence of the proof it turns out that this is the imaginary part. | |
| Dec 26, 2019 at 13:29 | comment | added | Guest | Ok. I only have a question about the first line when you defined $v$: I know that $v(x, y)=\Im(f(z)) =\frac{f(z) - \overline {f(z)}} {2i}$. So, is your $v$ is the same as the imaginary part of $f$? According to what you wrote it is like having $v(x, y)=\frac{f(z) - \overline {f(\bar{z} )}} {2i}$!!! | |
| Dec 26, 2019 at 13:17 | history | edited | Alexandre Eremenko | CC BY-SA 4.0 |
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| Dec 26, 2019 at 13:09 | comment | added | Alexandre Eremenko | @Guest: I made one more small correction, hopefully the last one. Now $b$ does not depend on he choice of $g$, only on $f$ itself. If you impose the condition that $a$ is pure imaginary, (include real part of $a$ into $g$) then the representation becomes canonical: $g$, $a$ and $b$ depend only of $f$. | |
| Dec 26, 2019 at 13:06 | history | edited | Alexandre Eremenko | CC BY-SA 4.0 |
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| Dec 26, 2019 at 10:31 | comment | added | Guest | the content $b$ depends on the choice of the function $g$, is this wright? | |
| Dec 26, 2019 at 4:20 | comment | added | Alexandre Eremenko | @Guest: thanks, I corrected. | |
| Dec 26, 2019 at 4:19 | history | edited | Alexandre Eremenko | CC BY-SA 4.0 |
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| Dec 26, 2019 at 4:12 | history | edited | Alexandre Eremenko | CC BY-SA 4.0 |
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| Dec 26, 2019 at 3:52 | history | edited | Alexandre Eremenko | CC BY-SA 4.0 |
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| Dec 26, 2019 at 3:48 | comment | added | Guest | thank you, this is true, and contains more. The function $f(z) =-iz=-ix+y$ satisfy the condition above but it is not real for real $z$. | |
| Dec 26, 2019 at 3:43 | history | undeleted | Alexandre Eremenko | ||
| Dec 25, 2019 at 22:48 | history | deleted | Alexandre Eremenko | via Vote | |
| Dec 25, 2019 at 22:33 | history | answered | Alexandre Eremenko | CC BY-SA 4.0 |