Orthogonal rational functions with poles on the unit circle (Q1323208)

Starting from a sequence of points on the unit circle the authors define the rational functions as the inverses of polynomials having the zeros in those points and a positive linear functional on the space of the considered rational functions. The orthogonal system of rational functions is obtained by orthogonalization of the rational functions defined above. The three term recurrence relation, the moment problem, the location of the zeros and the quadrature formulas connected with this orthogonal system are discussed.