Solution of a multiple Nevanlinna-Pick problem via orthogonal rational functions

We consider a Nevanlinna-Pick type interpolation problem for Caratheodory functions, where the values of the function and its derivatives up to certain orders are given at finitely many points of the unit disk. The set of all solutions of this problem is described by means of the orthogonal rational functions which play here a similar role as the orthogonal polynomials on the unit circle in the classical case of the trigonometric moment problem. In particular, we use a connection between Szego and Schur parameters which in the classical situation was discovered by Ja.L. Geronimus. (C) 2004 Elsevier Inc. All rights reserved.