Abstract
In this note, we present three independent results within generalized complex analysis (in the Colombeau sense). The first of them deals with non-removable singularities; we construct a generalized function u on an open subset Ω of C n , which is not a holomorphic generalized function on Ω but it is a holomorphic generalized function on Ω \ S, where S is a hypersurface contained in Ω. The second result shows the existence of a holomorphic generalized function with prescribed values in the zero-set of a classical holomorphic function. The last result states the existence of a compactly supported solution to the ∂¯ operator.