The Carathéodory–Fejér interpolation on the polydisc
We give an algorithm for finding a solution to the Carathéodory–Fejér interpolation problem on the polydisc, whenever a solution exists. A necessary condition for the existence of a solution becomes apparent from this algorithm. A generalization of the well-known theorem due to Nehari has been obtained. A proof of the Korányi–Pukánszky theorem also follows from these ideas.