Timeline for Residues of analytic operators
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Aug 13, 2023 at 9:01 | comment | added | Jochen Glueck | Sorry for being pedantic, but the edit still does not give the existence of the finite-rank map $P$, since $z \mapsto I - P_z$ could have an essential singularity at $z_0$. To get the map $P$ one also needs $I - P_{z_0}$ to be a Fredholm operator (or equivalently - as one has invertibility close to $z_0$ - a semi-Fredholm operator). | |
| Aug 12, 2023 at 15:20 | history | edited | M.González | CC BY-SA 4.0 |
typo
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| Aug 12, 2023 at 13:34 | history | edited | YCor |
edited tags
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| Aug 12, 2023 at 12:02 | comment | added | Igor Khavkine | From the way the question is written, it is not so clear what you are after. According to the question, $h$ is arbitrary, so it is not clear what information it could give you about the residue. If all you know is the approximate value of $z_0$, then you could use any of the usual iterative eigenvalue/eigenvector approximation methods. Also, as noted in the other comment, perhaps you meant to write $z_0$ for the eigenvalue, or set $z_0=1$. | |
| S Aug 12, 2023 at 11:41 | history | suggested | CommunityBot | CC BY-SA 4.0 |
the spetrum of $P_{z_0}$ possesses an isolated eigenvalue $1$ (assuming multiplicity is 1 and $I-P_z$ near $z_0$ is invertible).
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| Aug 11, 2023 at 19:49 | review | Suggested edits | |||
| S Aug 12, 2023 at 11:41 | |||||
| Aug 11, 2023 at 19:14 | comment | added | Jochen Glueck | There seem to be some assumptions missing. Under the given assumptions there doesn't need to exist such a projection $P$. In fact, $I-P_z$ need not even be invertible for $z$ close to $z_0$. (By the way, you probably want to replace $1$ with $\lambda$, but this doesn't fix the aforementioned issues.) | |
| Aug 11, 2023 at 18:45 | history | edited | LSpice | CC BY-SA 4.0 |
Capitalise title
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| S Aug 11, 2023 at 18:24 | review | First questions | |||
| Aug 12, 2023 at 7:15 | |||||
| S Aug 11, 2023 at 18:24 | history | asked | opera | CC BY-SA 4.0 |