In this paper we will prove a Mittag-Leffler type theorem for $\bar{\partial}$-closed $(0,n-1)$-forms in $\Bbb C^n$ by addressing the question of constructing such differential forms with prescribed periods in certain domains.
@article{119391, author = {Telemachos Hatziafratis}, title = {Mittag-Leffler type expansions of $\bar{\partial}$-closed $(0,n-1)$-forms in certain domains in $\Bbb C^n$}, journal = {Commentationes Mathematicae Universitatis Carolinae}, volume = {44}, year = {2003}, pages = {347-358}, zbl = {1127.32300}, mrnumber = {2026169}, language = {en}, url = {http://dml.mathdoc.fr/item/119391} }
Hatziafratis, Telemachos. Mittag-Leffler type expansions of $\bar{\partial}$-closed $(0,n-1)$-forms in certain domains in $\Bbb C^n$. Commentationes Mathematicae Universitatis Carolinae, Tome 44 (2003) pp. 347-358. http://gdmltest.u-ga.fr/item/119391/
On a class of $\bar{\partial}$-equations without solutions, Comment. Math. Univ. Carolinae 39.3 (1998), 503-509. (1998) | MR 1666762
Note on the Fourier-Laplace transform of $\bar{\partial}$-cohomology classes, Z. Anal. Anwendungen 17 (1998), 907-915. (1998) | MR 1669921
Expansions of certain $\bar{\partial}$-closed forms via Fourier-Laplace transform, preprint.
An Introduction to Complex Analysis in Several Variables, North-Holland, Amsterdam, 1990. | MR 1045639
Function Theory of Several Complex Variables, Wadsworth & Brooks/Cole, California, 1992. | MR 1162310 | Zbl 1087.32001
Holomorphic Functions and Integral Representations in Several Complex Variables, Springer-Verlag, New York, 1986. | MR 0847923 | Zbl 0591.32002