Timeline for Self-adjoint extensions for pseudo-differential operators
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 19, 2019 at 9:30 | history | edited | mcd | CC BY-SA 4.0 |
added 26 characters in body
|
| Feb 19, 2019 at 9:27 | comment | added | mcd | Yes, you are right, this is not a counterexample. | |
| Feb 18, 2019 at 15:00 | comment | added | Bazin | I have now strong doubts about your answer for the case $c=-1$ In fact, I believe that there is a self-adjoint extension in that case. | |
| Feb 11, 2019 at 9:39 | comment | added | Bazin | I looked at the Sjöstrand reference and did not see anything on the case $c\in (-\infty, 0)$. He studies in that book the case $c\in \mathbb C\backslash(-\infty, 0[$ which indeed are all non-self-adjoint if $c$ is not positive, but the case $c\in (-\infty, 0)$ is apparently not tackled in that reference. Thanks in advance for your help. | |
| Feb 8, 2019 at 19:57 | comment | added | Bazin | OK, I want ellipticity and the characteristic set to be a manifold, which is not the case of your example $\xi=\pm x$. | |
| Feb 8, 2019 at 16:36 | comment | added | mcd | In my example with $a_1(x,\xi) = \xi^2 - x^2$ and $a_0 = 0$, we have that $|\nabla p_2(x,\xi)|^2 = 4(\xi^2 + x^2)$, which is elliptic. | |
| Feb 8, 2019 at 15:50 | comment | added | Bazin | I mean that $a=a_1+a_0$ with $a_j\in \Sigma^j$ is such that $\vert \nabla a_1\vert^2$ is elliptic in $\Sigma_1$. | |
| Feb 8, 2019 at 15:44 | comment | added | mcd | What do you mean by principal symbol? Shubin or classical sense? | |
| Feb 8, 2019 at 15:40 | comment | added | Bazin | Thanks, I modified the question with a real principal type symbol $a$. | |
| Feb 8, 2019 at 15:31 | history | answered | mcd | CC BY-SA 4.0 |