Holomorphic extension of functions along finite families of complex straight lines in an n-circular domain

Resumo

We consider the continuous functions on the boundary of a bounded n-circular domain D in ℂⁿ, n > 1, which admit one-dimensional holomorphic extension along a family of complex straight lines passing through finitely many points of D. The question is addressed of the existence of a holomorphic extension of these functions to D.