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in 1959. This can be seen as an algebraic geometrization of analysis. It derives its meaning from the fact that the differential operator is right-invertible in several function spaces.
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and microfunctions. Semantically, it is the application of algebraic operations on analytic quantities. As a research programme, it was started by the
Japanese mathematician
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It helps in the simplification of the proofs due to an algebraic description of the problem considered.
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Not to be confused with the common phrase "algebraic analysis of ", meaning "the algebraic study of "
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221:{\displaystyle {\mathcal {H}}^{n}(\mu _{M}({\mathcal {O}}_{X})\otimes {\mathcal {or}}_{M/X})}
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Publications of the
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Technique of studying linear partial differential equations
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is the restriction of the sheaf of microfunctions to
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317:A microfunction can be used to define a Sato's
485:"Professor Mikio Sato and Microlocal Analysis"
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553:Foundations of algebraic analysis book review
41:to study properties and generalizations of
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541:Masaki Kashiwara and Algebraic Analysis
333:, in parallel to the fact the sheaf of
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122:be its complexification. The sheaf of
302:{\displaystyle {\mathcal {or}}_{M/X}}
31:linear partial differential equations
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341:is the restriction of the sheaf of
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648:Partial differential equations
321:. By definition, the sheaf of
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459:Kashiwara & Schapira 1990
581:. You can help Knowledge by
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658:Mathematical analysis stubs
518:. Berlin: Springer-Verlag.
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29:that deals with systems of
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447:Kashiwara & Kawai 2011
311:relative orientation sheaf
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383:Edge-of-the-wedge theorem
263:microlocalization functor
254:{\displaystyle \mu _{M}}
335:real-analytic functions
577:–related article is a
403:Gauss–Manin connection
393:Localization of a ring
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643:Generalized functions
575:mathematical analysis
343:holomorphic functions
323:Sato's hyperfunctions
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516:Sheaves on Manifolds
461:, Definition 11.5.1.
408:Differential algebra
378:Generalized function
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124:microlocal functions
510:Kashiwara, Masaki;
505:– via EMS-PH.
373:Microlocal analysis
628:Algebraic analysis
546:2012-02-25 at the
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79:. You can help by
23:Algebraic analysis
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477:Kashiwara, Masaki
449:, pp. 11–17.
109:analytic manifold
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638:Fourier analysis
633:Complex analysis
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512:Schapira, Pierre
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47:hyperfunctions
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60:Microfunction
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653:Sheaf theory
583:expanding it
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495:(1): 11–17.
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261:denotes the
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81:adding to it
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35:sheaf theory
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27:mathematics
622:Categories
418:Mikio Sato
118:, and let
51:Mikio Sato
434:Citations
243:μ
188:⊗
159:μ
113:dimension
43:functions
33:by using
544:Archived
514:(1990).
483:(2011).
368:D-module
357:See also
45:such as
469:Sources
309:is the
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231:where
573:This
103:be a
579:stub
520:ISBN
105:real
99:Let
37:and
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349:to
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