Minimal dimension families of complex lines sufficient for holomorphic extension of functions
Let \(\mathcal L_\Gamma\) be a family of complex lines in \(\mathbb C^n\) that pass through a given complex manifold \(\Gamma\) in a given direction \(b\). Let \(D\) be a bounded simply connected domain with connected boundary of class \(\mathcal C^2\) whose closure does not intersect \(\Gamma\). Then a function \(f\in \mathcal C(\partial D)\) is said to enjoy the one-dimensional extension property if \(f\) restricted to any \(l\in\mathcal L_\Gamma\) extends holomorphically to \(l\cap D\). The authors study the existence of holomorphic extensions of functions with one-dimensional extension property using the technique of Bochner-Martinelli integrals.
scientific article; zbMATH DE number 5912833
scientific article