On the problem of the linear conjugation for analytic functions in a bidisk

The problem of finding two functions phi(z) and psi(w) analytic on thr discs \z\ < 1 and \w\ < 1 respectively which satisfy thr functional equation is considered: where Omega is a Riemann surface defined by the non-reducible algebraic correspondence A(z,w) = 0. For the investigation of this problem is proposed a method based on the global uniformization of the correspondence A(z,w) = 0.