Timeline for Green's operator of elliptic differential operator
Current License: CC BY-SA 3.0
23 events
| when toggle format | what | by | license | comment | |
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| Dec 15, 2014 at 4:21 | vote | accept | mdg | ||
| S Dec 15, 2014 at 4:20 | history | bounty ended | mdg | ||
| S Dec 15, 2014 at 4:20 | history | notice removed | mdg | ||
| Dec 9, 2014 at 11:20 | answer | added | user80744 | timeline score: 11 | |
| Dec 8, 2014 at 20:07 | history | edited | mdg | CC BY-SA 3.0 |
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| Dec 8, 2014 at 17:39 | comment | added | Pedro Lauridsen Ribeiro | An implicit assumption in the question is that the base manifold $M$ should be compact, otherwise the operator cannot be Fredholm. Moreover, one only gets the tame estimates needed for Nash-Moser under this assumption. It is satisfied in the examples given, but it's not explicitly stated. | |
| Dec 8, 2014 at 17:35 | answer | added | Deane Yang | timeline score: 7 | |
| Dec 8, 2014 at 11:03 | comment | added | Igor Khavkine | If you use the inclusion $i \colon \operatorname{ker} P \to \Gamma(\cdots)$ and the orthogonal projection $j \colon \Gamma(\cdots) \to \operatorname{coker} P$, then $G$ is precisely the "pseudoinverse" that I mentioned in my answer. Other choices of $i, j, M$ and $N$ simply parametrize the many different ways one can define an "inverse" of a non-invertible linear operator. That last issue has nothing in particular to do with elliptic operators or functional analysis. It is an issue of ordinary linear algebra. | |
| Dec 8, 2014 at 9:46 | comment | added | mdg | So I think the second question is the same as the first - I'd like to construct the Green's operator of $P$. | |
| Dec 8, 2014 at 9:17 | comment | added | mdg | Basically I'm trying to verify a step in a paper by Hamilton, which essentially says "use the Green's operator" of the map $P$ above. One can only assume that by the Green's operator of $P$, Hamilton means the definition in his paper in the Nash-Moser theorem, which is written at about the same time as the paper I'm reading. | |
| Dec 8, 2014 at 9:11 | comment | added | Igor Khavkine | Your additional question is substantially different from the original, since you seem to be interested in the Nash-Moser inverse function theorem now. I suggest you ask it as a separate question. Also, you haven't made it clear how you intend to interpret the inverse (aka the Green operator) or a non injective/surjective differential operator. | |
| S Dec 8, 2014 at 5:09 | history | bounty started | mdg | ||
| S Dec 8, 2014 at 5:09 | history | notice added | mdg | Authoritative reference needed | |
| Dec 8, 2014 at 5:07 | history | edited | mdg | CC BY-SA 3.0 |
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| Dec 5, 2014 at 21:28 | history | edited | Vít Tuček | CC BY-SA 3.0 |
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| Dec 4, 2014 at 17:56 | answer | added | Igor Khavkine | timeline score: 4 | |
| Dec 4, 2014 at 12:17 | history | edited | user9072 | CC BY-SA 3.0 |
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| Dec 4, 2014 at 12:05 | answer | added | asv | timeline score: 3 | |
| Dec 4, 2014 at 7:00 | history | edited | mdg | CC BY-SA 3.0 |
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| Dec 4, 2014 at 5:23 | history | edited | mdg | CC BY-SA 3.0 |
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| Dec 4, 2014 at 5:13 | history | edited | mdg | CC BY-SA 3.0 |
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| Dec 4, 2014 at 3:51 | history | edited | mdg |
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| Dec 4, 2014 at 3:41 | history | asked | mdg | CC BY-SA 3.0 |