Approximation properties of holomorphic pairs of differential forms

Abstract

This article is devoted to the study of approximative properties of pairs of forms (wr −1,wr +1), of degrees (r − 1) and (r + 1), respectively, which satisfies the equations in some open set of an Euclidean space of finite dimension. We call such pairs holomorphic pairs of differential forms. For these pairs, two theorems, analogous to the classical Runge Theorem and to the Hartogs–Rosenthal theorem, respectively, are obtained.