Timeline for Sobolev density of smooth functions which are zero on a measure zero subset
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 15, 2022 at 15:10 | comment | added | Nate Eldredge | Right, but the set consisting of only the zero function is obviously not dense in Sobolev space. So what I mean is that unless you have more conditions on the set $A$, there is a trivial counterexample. Jan Bohr shows that there are also nontrivial counterexamples. | |
| Nov 15, 2022 at 13:03 | comment | added | Ryan Vaughn | I was wondering if the subspace of smooth functions which are zero on A is dense as a subspace of Sobolev space. It seems like that need not be the case, due to the answer below. | |
| Nov 15, 2022 at 6:21 | comment | added | Nate Eldredge | Did you want $A$ to be closed, or something like that? If $A$ is a dense set of measure zero then the set of smooth functions zero on $A$ is just $\{0\}$. | |
| Nov 15, 2022 at 0:23 | history | became hot network question | |||
| Nov 14, 2022 at 16:43 | answer | added | Jan Bohr | timeline score: 6 | |
| Nov 14, 2022 at 16:23 | history | asked | Ryan Vaughn | CC BY-SA 4.0 |