The Carathéodory-Fejér interpolation problem for the polydisc

Abstract

We give an algorithm for finding a solution to the Carathéodory-Fejér 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 Korányi--Pukánszky theorem is given using the spectral theorem.

20 pages