Article
Keywords:
Mittag-Leffler type expansions; $\bar{\partial}$-closed forms; Bochner-Martinelli kernel
Summary:
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.
References:
                        
[1] Hatziafratis T.: 
On a class of $\bar{\partial}$-equations without solutions. Comment. Math. Univ. Carolinae 39.3 (1998), 503-509. 
MR 1666762[2] Hatziafratis T.: 
Note on the Fourier-Laplace transform of $\bar{\partial}$-cohomology classes. Z. Anal. Anwendungen 17 (1998), 907-915. 
DOI 10.4171/ZAA/858 | 
MR 1669921[3] Hatziafratis T.: Expansions of certain $\bar{\partial}$-closed forms via Fourier-Laplace transform. preprint.
[4] Hörmander L.: 
An Introduction to Complex Analysis in Several Variables. North-Holland, Amsterdam, 1990. 
MR 1045639[5] Krantz S.: 
Function Theory of Several Complex Variables. Wadsworth & Brooks/Cole, California, 1992. 
MR 1162310 | 
Zbl 1087.32001[6] Range R.M.: 
Holomorphic Functions and Integral Representations in Several Complex Variables. Springer-Verlag, New York, 1986. 
MR 0847923 | 
Zbl 0591.32002