Timeline for Log-nonexpansive functions: terminology and references
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 14, 2012 at 7:45 | comment | added | Suvrit | Thanks Robert for this result; I did not know this theorem, but it seems that I might be able to use it. :-) | |
| Sep 14, 2012 at 3:10 | comment | added | Robert Israel | $g$ is non-expansive (in the usual metric on $\mathbb R$) iff $g(x) = g(0) + \int_0^x u(t)\ dt$ where $u$ is a measurable function with $|u| \le 1$ almost everywhere. | |
| Sep 13, 2012 at 7:57 | comment | added | Suvrit | @Robert: True! I had thought of doing a variable change, but ultimately, I am searching for sufficient conditions that allow one to easily test nonexpansivity for at least a class of functions. And a variable change merely pushes the burden of testing into a different metric.... :-) | |
| Sep 13, 2012 at 6:57 | answer | added | Dirk | timeline score: 1 | |
| Sep 13, 2012 at 0:01 | comment | added | Robert Israel | If you write $g(x) = \log h(e^x)$, so $g$ is a continuous function from $\mathbb R$ to itself, your condition is equivalent to $g$ being non-expansive in the usual metric on $\mathbb R$. | |
| Sep 12, 2012 at 20:49 | history | asked | Suvrit | CC BY-SA 3.0 |