On the existence of para-orthogonal rational functions on the unit circle
Abstract Similar as in the classical case of polynomials, as is known, para-orthogonal rational functions on the unit circle can be used to obtain quadrature formulas of Szegő-type to approximate some integrals. In the present paper we carry out a thorough discussion of the existence of such rational functions in terms of the underlying Borel measure on the unit circle.