Timeline for Bezout’s identity for analytic functions of several variables
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 18, 2021 at 20:48 | vote | accept | Jack L. | ||
| Jan 18, 2021 at 7:32 | answer | added | abx | timeline score: 8 | |
| Jan 18, 2021 at 6:56 | comment | added | Alexandre Eremenko | See "Cousin Problems" on Wikipedia, First Cousin's Problem. | |
| Jan 18, 2021 at 6:56 | comment | added | Alexandre Eremenko | @Daniele Tampieri: The crucial requirement that makes Corona non-trivial is that the functions must be bounded. The answer to the question is positive. | |
| Jan 18, 2021 at 6:38 | answer | added | Alexandre Eremenko | timeline score: 8 | |
| Jan 17, 2021 at 15:06 | comment | added | Jack L. | @Alexandre Eremenko: If the answer (to my question) is positive, could you write out a proof as answer or suggest a reference instead? Many thanks. | |
| Jan 17, 2021 at 13:29 | comment | added | Jack L. | @Wojowu: I have edited the question to avoid using the $\gcd$. | |
| Jan 17, 2021 at 13:27 | history | edited | Jack L. | CC BY-SA 4.0 |
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| Jan 17, 2021 at 13:12 | comment | added | Wojowu | The gcd as you define it will usually not exist - there is no holomorphic function which vanishes precisely when $z_1=z_2=0$. More generally the vanishing set cannot have codimension higher than $1$, which a vanishing set of two functions will almost always have) | |
| Jan 17, 2021 at 13:11 | comment | added | Jack L. | @Wojowu: I had thought about that — whether there always exist a $\gcd$; thanks for pointing this out. I’d rephrase the problem on that assumption. | |
| Jan 17, 2021 at 13:05 | comment | added | Wojowu | Is it implied here that the gcd exists? Because in several variables this need not be the case with your definition. | |
| Jan 17, 2021 at 13:04 | comment | added | Daniele Tampieri | This seems to be a SCV version of the corona theorem: I am not sure about the state of the art for this result, but by googling you'll get a fairly large number of examples. | |
| Jan 17, 2021 at 12:56 | history | asked | Jack L. | CC BY-SA 4.0 |