Timeline for Gluing together holomorphic functions without Mergelyan theorem
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| May 6, 2021 at 15:17 | comment | added | Joe | I mean: we have two functions, holomorphic on two different regions, which share some piece of boundary; is it possible to create a single holomorphic function approximating the given two on their respective domain? It is what I "smoothly" did in the post. I just need to do that holomorphically. | |
| May 6, 2021 at 8:10 | comment | added | Luka Thaler | Can you be more precise, what do you mean by gluing. In general there is no hope that the approximating function F would agree with g or h on some open set. | |
| May 6, 2021 at 7:26 | comment | added | Joe | Of course Mergelyan applies. I don't want to use it since I am writing a sort of generalization of it, which starts from the above explained setting. | |
| May 6, 2021 at 2:45 | comment | added | Alexandre Eremenko | Why do you need a proof WITHOUT Mergelian's theorem? | |
| May 5, 2021 at 23:55 | comment | added | Steven Gubkin | @Joe Why don't you think Mergelyan's theorem applies? Isn't $\Omega = \Delta \cup \Gamma$ compact, and $f$ holomorphic on the interior of $\Omega$? | |
| May 5, 2021 at 23:07 | history | edited | Joe | CC BY-SA 4.0 |
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| May 5, 2021 at 15:35 | comment | added | Joe | yes, uniform on compacts | |
| May 5, 2021 at 13:42 | comment | added | Pietro Majer | You mean uniform approximation, not stronger, right? | |
| May 5, 2021 at 13:08 | history | asked | Joe | CC BY-SA 4.0 |