Timeline for Build an explicit "small perturbation" of the identity satisfying some properties
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Dec 10, 2021 at 0:39 | vote | accept | CommunityBot | ||
| Dec 8, 2021 at 0:41 | comment | added | Willie Wong | In what is now the final condition, the implicit constant in the $\lesssim \epsilon$, will you allow it to depend on the interval $[a,b]$? If yes, then Iosif's answer does the job. It not (if you want the bound to be uniform over different intervals) I think it is probably doable but will require more work. | |
| Dec 7, 2021 at 23:18 | review | Close votes | |||
| Dec 12, 2021 at 3:11 | |||||
| Dec 7, 2021 at 22:42 | answer | added | Iosif Pinelis | timeline score: 0 | |
| Dec 7, 2021 at 20:07 | comment | added | user139844 | @WillieWong What if I drop the 4th condition? | |
| Dec 7, 2021 at 20:07 | history | edited | user139844 | CC BY-SA 4.0 |
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| Dec 7, 2021 at 19:44 | comment | added | Willie Wong | I am pretty sure if you apply Gronwall's Lemma to the fourth inequality, that $|x f''_\epsilon(x)| \leq f'(\epsilon)(x)$, and the fifth condition on $f_{\epsilon}$ being constant on an interval, together these will require $f_{\epsilon}$ to be identically constant. This makes the "approximation of identity" property impossible. | |
| Dec 7, 2021 at 17:50 | history | edited | user139844 | CC BY-SA 4.0 |
edited body
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| Dec 7, 2021 at 17:44 | history | asked | user139844 | CC BY-SA 4.0 |