Timeline for Is there a non-Shih analog for holomorphic functions of the Intermediate Value Theorem?
Current License: CC BY-SA 3.0
6 events
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| Sep 7, 2015 at 18:15 | history | edited | Alexandre Eremenko | CC BY-SA 3.0 |
added 72 characters in body
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| Sep 7, 2015 at 18:14 | comment | added | Alexandre Eremenko | @Simon Henry: you are right. I thought that this was stated in the question but now I see it was not:-) | |
| Sep 7, 2015 at 18:12 | comment | added | Alexandre Eremenko | Your sufficient condition is not stated clearly in this remark, but perhaps if you state it clearly it will become correct. | |
| Sep 7, 2015 at 15:00 | comment | added | student | I used the expression "number of zeros of the identity in $f(C)$" to denote the winding number of $f(C)$ around zero. Then (it seems to me) the equality I mentioned holds for holomorphic functions, and then one version of the condition I asked for would be (as I said) that $f(C)$ passes through all four quadrants in cyclic order--this is just a condition on the real and imaginary parts of $f(z), z \in C$. Is this indeed a sufficient condition to conclude that the open set bounded by $C$ contains a zero of $f$? | |
| Sep 7, 2015 at 13:14 | comment | added | Simon Henry | Of course, this only works if $f$ is defined on all the 'interior' of the curve. | |
| Sep 7, 2015 at 12:56 | history | answered | Alexandre Eremenko | CC BY-SA 3.0 |