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Involutivity of truncated microsupports. (English) Zbl 1035.35003

The notion of truncated microsupport is a suitable variant of the initial notion of microsupport of sheaves. In this paper the involutivity of the microsupport is studied. In general this property fails for truncated microsupport, but some week form of it holds. In this paper it is proved that the truncated microsupport is stable by Poisson bracket, i.e. if two functions vanish on it, their Poisson bracket vanishes, too. A result of J.-M. Bony about the same property for the normal cone to a closed subset is used in the proposed proof.

MSC:

35A27 Microlocal methods and methods of sheaf theory and homological algebra applied to PDEs
32C38 Sheaves of differential operators and their modules, \(D\)-modules
58J15 Relations of PDEs on manifolds with hyperfunctions
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