ガロア第一論文と乗数イデアル他関連資料スレ6

[過去ﾛｸﾞ] ガロア第一論文と乗数イデアル他関連資料スレ6 (1002ﾚｽ)
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53: １３２人目の素数さん [] 2024/01/14(日) 23:46:20.10 ID:9ByocRDs

>>50
>微分方程式がどうこういうんなら
>SKKよりハーン・バナッハの拡張定理の方が大事

これは御大か
不勉強で下記を最近知りました
”The original proofs of Malgrange and Ehrenpreis were non-constructive as they used the Hahn–Banach theorem.”

(参考)
https://en.wikipedia.org/wiki/Malgrange%E2%80%93Ehrenpreis_theorem
Malgrange–Ehrenpreis theorem

Proofs
The original proofs of Malgrange and Ehrenpreis were non-constructive as they used the Hahn–Banach theorem. Since then several constructive proofs have been found.

There is a very short proof using the Fourier transform and the Bernstein–Sato polynomial, as follows.
略
A short constructive proof was presented in (Wagner 2009, Proposition 1, p. 458):
略

https://en.wikipedia.org/wiki/Hahn%E2%80%93Banach_theorem
The Hahn–Banach theorem is a central tool in functional analysis. It allows the extension of bounded linear functionals defined on a vector subspace of some vector space to the whole space, and it also shows that there are "enough" continuous linear functionals defined on every normed vector space to make the study of the dual space "interesting".

http://rio2016.5ch.net/test/read.cgi/math/1704672583/53

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