Timeline for What essential property justifies the name "derivative"?
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 9, 2019 at 14:31 | comment | added | LSpice | @SteveHuntsman, OK, I see. | |
| Jan 9, 2019 at 9:54 | comment | added | Steve Huntsman | @LSpice 'finite' is taken in the usual sense. IIRC I was trying to emphasize the Banach algebra structure, which more generally requires boundedness as an explicit condition | |
| Jan 9, 2019 at 2:12 | comment | added | LSpice | @SteveHuntsman, does 'finite' here mean something other than the usual set-theoretic notion? Otherwise it's hard to know what else a (real- or complex-valued) function on a finite set could be than bounded. | |
| Jan 31, 2012 at 21:57 | comment | added | Victor Dods | Thank you Mariano, that's a really neat and apropos result. | |
| Jan 31, 2012 at 21:56 | history | edited | Victor Dods | CC BY-SA 3.0 |
typo in LaTeX code
|
| Jan 30, 2012 at 3:17 | comment | added | Steve Huntsman | Re: my comment above, see mathoverflow.net/questions/32667/… | |
| Jan 30, 2012 at 3:15 | comment | added | Steve Huntsman | A notion of derivative applies for functions on many finite sets in $\mathbb{R}^n$ (say). Though the Banach algebra of bounded functions on a finite set turns out to carry no nonzero derivations, one can pick a suitable function space for which the interpolation problem has a unique solution and differentiate the interpolant. This is intrinsically non-local. | |
| Jan 30, 2012 at 0:33 | comment | added | Mariano Suárez-Álvarez | As for «what's the essential quality of a differential operator», one answer is Peetre's theorem. (Wikipedia's write-up on this is particularly obfuscated, so Googling a bit might be helpful) | |
| Jan 30, 2012 at 0:29 | comment | added | Tom Goodwillie | Yes, pseudo-differential operators are defined by convolution and are somehow not local but very close to being local. | |
| Jan 30, 2012 at 0:16 | comment | added | Mariano Suárez-Álvarez | A keyword you might search for is pseudo-differential operators, which is usually attached to well-behaved operators in that spirit... | |
| Jan 30, 2012 at 0:04 | history | asked | Victor Dods | CC BY-SA 3.0 |