Timeline for What do people call functionals on holomorphic functions and on polynomials?
Current License: CC BY-SA 4.0
8 events
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| Nov 18, 2021 at 10:20 | comment | added | Sergei Akbarov | Actually, I don't like the name "analytic functional", because it's impossible to explain in which sense it is analytic. This is like "smooth functional" for $f:\mathcal{E}(M)\to\mathbb{C}$. Such functionals, i.e. distributions, usually are not smooth. I expected there are better terms. | |
| Nov 17, 2021 at 23:48 | comment | added | Alexandre Eremenko | This I do not know. | |
| Nov 17, 2021 at 23:42 | comment | added | Sergei Akbarov | @AlexandreEremenko thank you. And what is the term for functionals on $\mathcal{P}(M)$? | |
| Nov 17, 2021 at 23:22 | comment | added | Alexandre Eremenko | "Analytic functionals" is a standard name. See, Hormander, The analysis of linear partial differential operators I, Chap. 9. | |
| Nov 17, 2021 at 19:54 | comment | added | Sergei Akbarov | @DavidLoeffler yes, this sounds logical, but, to tell the truth, the terms "algebraic distribution", "holomorphic distribution", "smooth distribution", "continuous distribution" are strange as well... "Holomorphic distribution" does not seem to be holomorphic in any reasonable sense. Similarly, "algebraic distribution", etc. | |
| Nov 17, 2021 at 19:43 | comment | added | David Loeffler | In p-adic functional analysis it's conventional that the dual of the space of "[whatever] functions" gets called the space of "[whatever] distributions" (with measures being the exception to this convention). Not sure if this is a general convention though. I'd certainly use "algebraic distributions" for the dual of your $\mathcal{P}(M)$. | |
| Nov 17, 2021 at 19:26 | history | edited | Sergei Akbarov | CC BY-SA 4.0 |
added 69 characters in body
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| Nov 17, 2021 at 19:20 | history | asked | Sergei Akbarov | CC BY-SA 4.0 |