Multidimensional Boundary Morera Theorems in Matrix Domains

This survey considers continuous functions defined on the boundary of a bounded domain D in \({\mathbb{C}}^{n}\) ${\mathbb{C}}^n$ , n > 1, and possessing the Morera boundary property. We study the question of the existence of a holomorphic extension of such functions into the domain D for some sufficient sets Γ of complex lines.