Some results for the \(\overline{\partial}\) operator on generalized differential forms (Q1323118)

The paper is concerned with the \(\overline\partial\) operator on generalized differential forms. The notion of generalized function is the one of the Colombeau algebra on an open set [see e.g. \textit{H. Biagioni}: ``A nonlinear theory of generalized functions'', Lect. Notes Math. 1421 (1990; Zbl 0694.46032)]. The first Cousin problem is introduced in this setting. The author then extends earlier results of his [Proc. Lond. Math. Soc., III. Ser. 53, 474-488 (1986; Zbl 0652.35014)] to the case of \((0,q)\)-forms with \(q\geq 1\).