Timeline for Clarification about extensions of Ornstein-Uhlenbeck operator
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Mar 6, 2021 at 10:24 | comment | added | Giorgio Metafune | Yes true, but you can check that is a core directly: the Schwartz class is a core, since it is invariant under the semigroup and approximating a function in the Schwartz class with functions with compact support, in the graph norm, is not a problem. | |
| Mar 6, 2021 at 10:11 | comment | added | user69642 | @Giorgio: thank you for your comment. Indeed, once you have identified the domain of $\mathcal{L}_p$ as the Sobolev space $W^{2,p}(\gamma)$ and prove that $\mathcal{C}_c^{\infty}(\mathbb{R})$ is dense in $W^{2,p}(\gamma)$, you are done. I guess it is contained in your papers '02 regarding OU. Thanks again | |
| Mar 6, 2021 at 10:00 | comment | added | Giorgio Metafune | Yes, they are the same. The reason is that $C_c^\infty(R^d)$ is a core for ${\cal L}_p$. I can give a reference if you don't find it. | |
| Mar 5, 2021 at 18:44 | history | edited | gmvh | CC BY-SA 4.0 |
Fixed typo in title
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| Mar 5, 2021 at 18:10 | history | asked | user69642 | CC BY-SA 4.0 |