Timeline for History of Sobolev space notations
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 4, 2019 at 15:05 | answer | added | AbuSaad | timeline score: 0 | |
| Aug 18, 2017 at 3:51 | answer | added | Mostafa Jani | timeline score: 1 | |
| Aug 29, 2012 at 2:41 | vote | accept | timur | ||
| Aug 29, 2012 at 2:41 | history | bounty ended | timur | ||
| Aug 27, 2012 at 14:33 | comment | added | B R | @Bazin, interesting! Rereading my previous comment, I think it falls rather flat and seems to imply that Nate would not have already known the content. Since you reference it, though, I cannot now delete it! :) | |
| Aug 27, 2012 at 12:29 | answer | added | Carlo Beenakker | timeline score: 12 | |
| Aug 23, 2012 at 11:47 | comment | added | Bazin | @BR I guess the cyrillic letter for S reads C. About the Schwartz space $\mathscr S(\mathbb R^n)$: Laurent Schwartz defined that space in the mid-forties and the letter S was not after his own name, but did stand at the time for ``Spherical functions'' which are smooth functions defined on the sphere with $n$ dimensions and that are flat at the north pole (all derivatives vanish there). By stereographic projection, you recover what is now known as the Schwartz space. | |
| Aug 23, 2012 at 0:52 | history | bounty started | timur | ||
| Mar 8, 2012 at 8:14 | comment | added | Theo Buehler | According to Pietro Majer (comment to this answer mathoverflow.net/questions/1890/…) the $H$ is a Russian en standing for S.M. Nikolsky. | |
| Mar 8, 2012 at 8:09 | comment | added | Denis Serre | @Nate. When I graduated, I found a humoristic picture about pure and applied mathematicians. One mathematical child is piling up cohomology groups (there are arrows), while another is lining up Sobolev spaces (with embedding arrows). The idea was that pure maths goes to the heavens, whereas applied maths are down-to-earth. | |
| Mar 8, 2012 at 4:26 | comment | added | timur | @Nate, $H$ is also used for the Bessel potential version of Sobolev spaces that are $L^p$-based (but this was probably inspired by the already existing notation for the $L^2$-based case). Actually, the Hardy space notation $H^p$ might predate the Sobolev spaces. | |
| Mar 8, 2012 at 4:18 | comment | added | B R | Nate, $S$ is also already the Schwartz space. | |
| Mar 8, 2012 at 2:49 | comment | added | Nate Eldredge | Note that (in my experience) $H$ is only used for Sobolev spaces with $p=2$, which are Hilbert spaces. Also, $S^n$ already means "sphere". (Granted, $H^n$ might mean "cohomology"...) | |
| Mar 8, 2012 at 1:40 | history | asked | timur | CC BY-SA 3.0 |