The computation of orthogonal rational functions and their interpolating properties (Q1183327)

The authors present orthogonal basis functions of nested spaces \({\mathcal L}_ n\), \(n=0,1,2,\dots\) of rational functions with \(n\) prescribed poles for a general positive measure on the unit circle. They develop a Szegö type recurrence relation for the orthogonal rational functions and concentrate on the functions of the second kind, which are natural generalizations of the Szegö polynomials. In the last section, an algorithm of the Nevanlinna-Pick type is developed to find the recursion coefficients.