sheaves of pseudoanalytic differential forms

A way to extend the notion of pseudoanalyticity of the Bers-Vekua theory to differential forms defined on a complex manifold is presented, defining a sheaf whose sections over an open subset are differential forms whose component functions with respect to any trivializing sections induced by a local coordinate system satisfy in each argument the complex-linear Carleman-Bers-Vekua equation; such a sheaf may be defined as the kernel sheaf of an appropriate sheaf homomorphism, for which, under certain conditions an analogue of the Poincaré lemma holds and, under the same conditions, the sequence of such sheaf homomorphisms forms a complex, all of which allows one to prove an analogue of the Dolbeault’s theorem for these sheaves.

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