Representation of hyperfunction solutions in a hypo-analytic structure (Q1568804)

In this paper, the author analyzed the local structure of the hyperfunction solutions in a hypo-analytic manifold. Such class of solutions, which generalizes both the notion of (distribution) solutions to systems of vector fields associated to locally integrable structure and of hyperfunctions defined in a maximally real submanifold of the complex space. By using the FBI transform, the author got an elementary proof of the expected regularity for the solutions of an operator in the Kaneko's class acting on a maximally real submanifold of the complex space, and proved a result on representation of hyperfunction solutions on hypo-analytic structure which is a generalization of a former result due to Baouendi-Treves in the classical set-up, and furthermore proved that in a hypercomplex structure all hyperfunction solutions are necessarily hypo-analytic. Finally, the author extended further the results to cohomology classes of the differential complex naturally associated to a given hypo-analytic structure.