Timeline for Partial well-posedness results on Schrödinger operators?
Current License: CC BY-SA 4.0
9 events
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| Sep 25, 2019 at 14:40 | comment | added | Yidong Luo | @JochenGlueck Can this way yield an explicit expression for one infinite-dimensional range? | |
| Sep 25, 2019 at 14:24 | comment | added | Jochen Glueck | You can, for instance, integrate the spectral measure of your operator over the constant function with value $1$ over any subset of the spectrum that does not contain $0$ in its closure; the result will be a spectral projection $P$ such that the restriction of your operator to the range of $P$ is countinuously invertible. Hence, $\mathcal{B}_i$ can be chosen as the range of any such projection $P$. | |
| Sep 25, 2019 at 14:21 | history | edited | Arun Debray | CC BY-SA 4.0 |
\"{o} -> ö hopefully makes this easier to search for
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| Sep 25, 2019 at 13:14 | comment | added | Yidong Luo | @JochenGlueck This is a naive example i ignore. Ok, now the focus is on the infinite-dimensional case. Is there some known research on it? | |
| Sep 25, 2019 at 13:09 | comment | added | Jochen Glueck | Well, every linear operator from a finite dimensional space to any normed space is continuous, so you can choose $\mathcal{B}_i$ to be any finite dimensional subspace of $\mathcal{R}(A_i)$ and the restriction of $A_i^{-1}$ to $\mathcal{B}_i$ will be continuous. | |
| Sep 25, 2019 at 11:51 | comment | added | Yidong Luo | @JochenGlueck Now i have no mature thoughts. Maybe you can give me some examples to feel? Even the finite dimensional case will be welcome. Of course the bigger and infinite-dimensional will be better. | |
| Sep 25, 2019 at 11:19 | comment | added | Jochen Glueck | What kind if conditions do you want $\mathcal{B}_i$ to satisfy? For instance, the situation becomes trivial if you allow finite-dimensional $\mathcal{B}_i$. | |
| Sep 25, 2019 at 10:11 | history | edited | Yidong Luo | CC BY-SA 4.0 |
added 2 characters in body
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| Sep 25, 2019 at 9:36 | history | asked | Yidong Luo | CC BY-SA 4.0 |