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Microlocalisation tempérée. Application aux distributions holonômes sur une variété complexe. (Tempered microlocalization. Application to holonomic distributions on a complex variety). (French) Zbl 0655.35005
Sémin., Équations Dériv. Partielles 1987-1988, Exp. No. 2, 10 p. (1988).
Author’s summary: Let X be a smooth complex manifold. The T-$$\mu$$ $${\mathcal H}om(.,{\mathcal O}_ X)$$ functor, which is the micro-local version of the RH(.) functor of Kashiwara, is a version with growth condition of the $$\mu$$ $${\mathcal H}om(.,{\mathcal O}_ X)$$ of Kashiwara-Shapira. It allows to build up temperate objects analoguous to those built in [S.K.K.] with their operations.
Canonical transforms operate on T-$$\mu$$ $${\mathcal H}om(.,{\mathcal O}_ X)$$. We show that they allow to microlocalize the conjugation functor of Kashiwara to prove that the wave front set of a distribution u on X which is solution of a regular holonomic $$D_ X$$-module coincide with the characteristic variety of $$D_ Xu$$.
Reviewer: D.Barlet
##### MSC:
 35A27 Microlocal methods and methods of sheaf theory and homological algebra applied to PDEs 35A30 Geometric theory, characteristics, transformations in context of PDEs 35A20 Analyticity in context of PDEs
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