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| {{merge to|Algebraic analysis|date=March 2019}} | {{merge to|Algebraic analysis|date=March 2019}} | ||
| '''Note''': This draft still doesn't define microfunction and not quite ready to be in | '''Note''': This draft still doesn't define microfunction and not quite ready to be in mainspace | ||
| ⚫ | ----- | ||
| Let ''M'' be a real-analytic manifold and ''X'' its complexification. | Let ''M'' be a real-analytic manifold and ''X'' its complexification. | ||
| ⚫ | ---- | ||
| By definition, the sheaf of ]s on ''M'' is the restriction of the sheaf of microfunctions to ''M'', in parallel to the fact the sheaf of real-analytic functions on ''M'' is the restriction of the sheaf of holomorphic functions on ''X'' to ''M''. | A microfunction can be used to define a hyper function. By definition, the sheaf of ]s on ''M'' is the restriction of the sheaf of microfunctions to ''M'', in parallel to the fact the sheaf of real-analytic functions on ''M'' is the restriction of the sheaf of holomorphic functions on ''X'' to ''M''. | ||
| == References == | == References == | ||
Revision as of 23:14, 10 March 2019
Comment: If it needs a better lede wrote the lede. Don't move war. Don't resist a merge. This page was up for G13 as abandoned. Do something with it. Legacypac (talk) 23:08, 10 March 2019 (UTC)
- I'm not resisting the merger; I was unaware of the past MfD discussion. Not just the lead but the definition is also missing; in short, more work is needed. -- Taku (talk) 23:11, 10 March 2019 (UTC)
 | It has been suggested that this page be merged into Algebraic analysis. (Discuss) Proposed since March 2019. |
Note: This draft still doesn't define microfunction and not quite ready to be in mainspace
Let M be a real-analytic manifold and X its complexification.
A microfunction can be used to define a hyper function. By definition, the sheaf of Sato's hyperfunctions on M is the restriction of the sheaf of microfunctions to M, in parallel to the fact the sheaf of real-analytic functions on M is the restriction of the sheaf of holomorphic functions on X to M.
References
- Masaki Kashiwara and Pierre Schapira: Sheaves on Manifolds. Springer-Verlag. Berlin Heidelberg New York.1990: ISBN 3-540-51861-4.
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