Analytic continuation of generalized functions (Q1113427)

The following result is proved: Let \(\Omega\) be a connected open non void set in \(C^ n\) and let F be a generalized holomorphic function on \(\Omega\) ; if F is null on a non void open subset of \(\Omega\), then F is null in \(\Omega\). The result was announced in \textit{J. F. Colombeau}: Elementary introduction to new generalized functions, North-Holland Math. Studies, No.113 (1985; Zbl 0584.46024), where a sketch of the proof in the case \(n=1\) was given.