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Mittag-Leffler type expansions of \(\bar {\partial }\)-closed \((0,n-1)\)-forms in certain domains in \(\mathbb C^n\). (English) Zbl 1127.32300

The paper is devoted to the study of the problem of existence of differential \(\bar {\partial }\)-closed \((0, n - 1)\) forms with given periods in some domains in \(\mathbb C^n\).
There are proved several Mittag-Leffler type theorems which can be used for constructions of such forms in pseudoconvex domains.
Also a description of \(\bar {\partial }\)-cohomology groups \(H^{(0, n - 1)}_{\bar {\partial }} (D - A)\), \(D\) open pseudoconvex, \(A\) discrete is given.

MSC:

32A25 Integral representations; canonical kernels (Szegő, Bergman, etc.)
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