Andronikof, E. 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 Keywords:smooth complex manifold; micro-local; functor of Kashiwara; growth condition; Canonical transforms; wave front set; regular holonomic; characteristic variety PDF BibTeX XML Full Text: Numdam