Timeline for Heat equation on torus
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 18, 2019 at 22:39 | comment | added | Mateusz Kwaśnicki | @AbdelmalekAbdesselam: That's interesting! I did not know this, I thought they only dealt with the $\alpha \le 2$ case. (This sort of confirms what one of my masters told me long ago: whatever you prove, there is a related result of one of "The Martians" – the result for $d = 1$ is due to Pólya...) | |
| Jun 18, 2019 at 21:29 | comment | added | Abdelmalek Abdesselam | BTW Thm 2.1 of the ref by Blumenthal and Getoor I gave in my other MO answer does prove the asymtotic expansiion and constant sign at infinity you mentioned. | |
| Jun 18, 2019 at 21:23 | comment | added | Abdelmalek Abdesselam | I figured you knew this but just typed too fast...I did too, I meant α≤2... | |
| Jun 18, 2019 at 21:09 | history | edited | Mateusz Kwaśnicki | CC BY-SA 4.0 |
added 1849 characters in body
|
| Jun 18, 2019 at 20:49 | comment | added | Mateusz Kwaśnicki | @AbdelmalekAbdesselam: Ah, actually all of my answer is about $\alpha \le 1$! Too sloppy again... Thanks! | |
| Jun 18, 2019 at 20:38 | comment | added | Abdelmalek Abdesselam | +1 but what you said about $p_t$ being a probability density (so its $L^1$ norm is 1 allowing for the use of Young's convolution inequality etc.) is only true if $\alpha\le 1$. See my answer to mathoverflow.net/questions/256526/… | |
| Jun 18, 2019 at 19:28 | history | answered | Mateusz Kwaśnicki | CC BY-SA 4.0 |