Timeline for Density of smooth functions under "Hölder metric"
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 17, 2013 at 14:57 | history | edited | Julián Aguirre | CC BY-SA 3.0 | edited body |
| Apr 6, 2013 at 18:14 | comment | added | Ben McKay | You want $\phi_{\varepsilon}(x)=\varepsilon^{-n}\phi(x/\varepsilon)$ to get a mollifier. | |
| Jul 3, 2010 at 22:14 | comment | added | Julián Aguirre | I have included some more detail, but I have also realizaed that it is not clear at all that $\lim_{\varepsilon\to0}G_\varepsilon(t)=0$. | |
| Jul 3, 2010 at 22:12 | history | edited | Julián Aguirre | CC BY-SA 2.5 | added 69 characters in body |
| Jul 3, 2010 at 21:42 | history | edited | Julián Aguirre | CC BY-SA 2.5 | Included more detail |
| Jul 2, 2010 at 5:23 | comment | added | Vince | Hi Julian, thanks for replying. I followed most of what you wrote, except I'm unclear about the last step. I am guessing you meant $g_\varepsilon$ in place of $g$? Could you please provide some insight as to how the inequality $\omega_\alpha(g_\varepsilon) \leq \int \phi(t)G_\varepsilon(t) dt$ holds? I ask because I thought I had a counterexample in mind in the boundary case of $\alpha = 1$, and it didn't seem like there was a dependence on the choice of $\alpha$, unless it appears in that particular inequality. Of course, I could be mistaken. | |
| Jul 1, 2010 at 18:02 | history | answered | Julián Aguirre | CC BY-SA 2.5 |