Timeline for Time averages and differentiability
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 22, 2018 at 23:11 | answer | added | Gabe K | timeline score: 3 | |
| Jul 27, 2016 at 14:13 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Jun 27, 2016 at 13:31 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Jun 17, 2016 at 12:34 | comment | added | alvarezpaiva | @KHughes it's not my paper to share. Write Francois. | |
| May 28, 2016 at 13:11 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Apr 28, 2016 at 15:20 | comment | added | user70229 | I too would be grateful! | |
| Jul 10, 2015 at 13:39 | comment | added | K Hughes | I would be grateful to see a copy if possible. Thanks! | |
| Jul 3, 2015 at 12:55 | comment | added | alvarezpaiva | The non-trivial result is equivalent to the statement that if $f$ is a continuous, real-valued function on the reals and $f(x+ T) - f(x)$ is smooth for every fixed $T$, then $f$ is smooth. I had asked this to my colleague, Jean-François Burnol and he gave a beautiful proof which, as he described, is an ode to Baire's theorem. He even proved it in the case $f$ is just assumed to be a distribution. I don't know if he published it or plans to publish it, but it is nicely written and you can ask him for a copy if you like. | |
| Jul 3, 2015 at 11:01 | comment | added | K Hughes | I don't expect this to be true as averaging tends to improve the regularity of a function. Do you have a reference for the non-trivial result in your remark? | |
| Jul 3, 2015 at 8:18 | history | edited | alvarezpaiva | CC BY-SA 3.0 |
Added some motivation.
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| Jul 3, 2015 at 8:05 | comment | added | alvarezpaiva | Not really. It only serves in pointing out that as T goes to zero, $A_T f(x) = f(x)$. The (very loose) analogy here is not with Birkhoff's ergodic theorem, but with Wiener's differentiation theorem. | |
| Jul 2, 2015 at 13:14 | comment | added | jesus | sorry for posting it as an answer, but i don't have the right to comment. since you are not requiring anything for the limit $T \rightarrow \infty $, the normalization of the time integral by $T^{-1} $ does not really serve a purpose, does it? | |
| Jun 29, 2015 at 13:01 | history | asked | alvarezpaiva | CC BY-SA 3.0 |