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On a theorem of Airapetyan and Henkin. (English) Zbl 0747.32011

The aim of this paper is to give a survey of some results and techniques that the author developed in the last years for the study of the tangential Cauchy-Riemann complex and that are alternative to the use of Henkin-Ramirez kernels, which apparently dominate complex analysis nowadays.
Contents: Introduction.
§1. Mayer-Vietoris exact sequences. A. Whitney sections. B. Differential complexes. C. Rough Mayer-Vietoris sequences with supports. C’. Duality between the two Mayer-Vietoris sequences on functions. D. Mayer-Vietoris sequences with supports for distributions. E. Extensible distributions. F. Duality between the Mayer-Vietoris sequences for distributions. G. Spectral sequence.
§2. Some results on Partial Differential Equations with constant coefficients.
§3. Analytic continuation of CR-functions and CR-forms.

MSC:

32W05 \(\overline\partial\) and \(\overline\partial\)-Neumann operators
32-02 Research exposition (monographs, survey articles) pertaining to several complex variables and analytic spaces
35N15 \(\overline\partial\)-Neumann problems and formal complexes in context of PDEs
32F10 \(q\)-convexity, \(q\)-concavity
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