Dolbeault’s theorem for sheaves of pseudoanalytic differential forms
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Irakli Sikharulidze
Abstract
A way is presented to extend the notion of pseudoanalyticity of the Bers–Vekua theory to differential forms defined on a complex manifold. A sheaf is defined whose sections over an open subset are differential forms whose component functions with respect to any trivializing sections satisfy in each argument the linear Carleman–Bers–Vekua equation. Such a sheaf can be defined as the kernel sheaf of an appropriate sheaf homomorphism. For it, under certain conditions, an analogue of the Poincaré lemma is valid and, under the same conditions, the sequence of such sheaf homomorphisms forms a complex, which makes is possible to prove an analogue of the Dolbeault’s theorem for these sheaves.
Funding statement: This work was supported by grant No. FR 22-354 from the Shota Rustaveli National Science Foundation.
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