It is not difficult to show that ifis an analytic function on the distinguished boundary, and on the diagonal of the polydisk inCn, then it is also analytic in the closed polydisk. This fact is used in order to give a complete solution to a problem implicit in Kim's work and partially solved by him and Wejntrob. In fact we prove: If the equation(where thepfs are analytic in a simply connected Jordan domainDand on its boundary ∂D, then (*) is disconjugate on [Dtilde]