Timeline for Question on whether, "An entire function, nowhere zero, has an entire logarithm," holds for matrix-valued entire functions as well
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 26, 2023 at 16:16 | comment | added | Robert Israel | Why don't you think it shows that? | |
| Dec 26, 2023 at 6:31 | comment | added | Kanghun Kim | It does not seem to show that all logarithms of A(z) are non-entire... | |
| Dec 25, 2023 at 18:54 | comment | added | Christian Remling | This is a nice simple argument. I had a slightly more complicated one, which however shows that there almost never will be an entire matrix logarithm: The eigenvalues $\lambda_j$ of $A$ will typically have Puiseux type branch points and hence so will those of $B$ (call them $\mu_j=\log\lambda_j$), but then $\prod\mu_j=\det B$ would have to be entire, which is unlikely. | |
| Dec 25, 2023 at 18:24 | history | edited | Robert Israel | CC BY-SA 4.0 |
added 16 characters in body
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| Dec 25, 2023 at 18:24 | comment | added | Robert Israel | Yes, it is a counterexample. | |
| Dec 25, 2023 at 18:23 | comment | added | Kanghun Kim | Looks like "proof by counterexample" to me... | |
| Dec 25, 2023 at 18:21 | history | answered | Robert Israel | CC BY-SA 4.0 |