Szegő-type quadrature formulas

We consider the approximation of integrals with respect to measures supported on the unit circle by means of positive quadrature formulas with maximal domain of exactness and up to three preassigned nodes. The quadrature formulas are exact in a new nested sequence of subspaces of Laurent polynomials that allows us to extend analogous properties to the usual quadrature formulas on the real line. Estimations for the error of these quadrature formulas depending on the regularity of the integrand are obtained.