The Carath\'eodory-Fej\'er interpolation problem for the polydisc

We give an algorithm for finding a solution to the Carath\'{e}odory-Fej\'{e}r interpolation problem on the polydisc $\mathbb D^n,$ whenever it 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 Kor\'{a}nyi--Puk\'{a}nszky theorem is given using the spectral theorem.