Necessary and sufficient conditions for the local solvability in hyperfunctions of a class of systems of complex vector fields
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- Cordaro, P.D. & Treves, F. Invent Math (1995) 120: 339. doi:10.1007/BF01241132
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A necessary and sufficient condition is proved for the validity of the Poincaré Lemma in degreeq≧1, in the differential complex attached to a locally integrable structure of codimension one, in spaces of hyperfunctions. The base manifold ℳ is only assumed to be smooth. The hyperfunctions are defined in the hypo-analytic structure associated to a smooth “first integral” Z. The condition is that the singular homology of the fibres of the map Z be trivial in dimensionq-1. By the approximation formula of [BT]|the germ of this fibration at a point is independent of the choice of the first integral Z.