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Analyse microlocale sur les variétés de Cauchy-Riemann et problème de Lewy pour les solutions hyperfonctions. (French) Zbl 0583.32035

This paper deals with the Lewy problem, i.e., the problem of holomorphic extensions of solutions of the tangential Cauchy-Riemann equation on a real analytic submanifold in a complex manifold and its generalization, from the algebraic analytic view point. The author reformulates the problem by using the language of \({\mathcal D}\)-modules and gives a necessary and sufficient condition for the Lewy problem for a real analytic hypersurface. Next, he considers a general system \({\mathcal M}\) on a complex manifold X satisfying \({\mathcal E}xt^ k_{{\mathcal D}_ X}({\mathcal M},{\mathcal O}_ X)=0\) and gives two equivalent conditions in order that any tangential holomorphic function on a real analytic hypersurface N is extended to a holomorphic solution of \({\mathcal M}\). Lastly, he gives some considerations when N is a subvariety of codimension more than two.
Reviewer: M.Muro

MSC:

32D15 Continuation of analytic objects in several complex variables
32V40 Real submanifolds in complex manifolds
32C36 Local cohomology of analytic spaces
32A45 Hyperfunctions
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