Timeline for A smooth function such that the second derivative of its absolute value is a distribution of positive order
Current License: CC BY-SA 4.0
5 events
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| May 28, 2021 at 12:39 | comment | added | Christian Remling | @MichaelRenardy: Yes, thanks, I figured it out in the meantime myself. (What confused me was the case of a more complicated zero set, say a Cantor set.) Maybe a more explicit version of the start of your argument would be to write $(g'',\varphi)=\int g\varphi'' = \int_{f\not= 0}g\varphi''$, and then we integrate by parts twice on each component of the open set $\{ f\not= 0\}$. | |
| May 28, 2021 at 11:51 | comment | added | Bazin | Very nice argument, thanks. | |
| May 27, 2021 at 22:21 | comment | added | Michael Renardy | $g''$ is a function on any interval where $f\neq 0$. Because on any such interval $g$ is either $f$ or $-f$. | |
| May 27, 2021 at 21:53 | comment | added | Christian Remling | Can you please explain the first claim in more detail. In particular, what is the precise meaning of "results from"? (If you are claiming that $g''$ is a function on some open set, what is that set?) | |
| May 27, 2021 at 18:59 | history | answered | Michael Renardy | CC BY-SA 4.0 |