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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
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
Full Text: Numdam