Gaussian quadrature formulae on the unit circle (Q1602773)

The authors construct quadrature formulae which are exact in a certain linear subspace of Laurent polynomials. The zeros of Szegő polynomials are chosen as nodes of the corresponding quadratures. Then, they use these formulae to estimate the integrals of the form \(I_\mu(f)=(1/2\pi) \int^{2 \pi}_0 f(e^{i\theta}) d\mu(\theta)\), where \(\mu\) is a probability measure on \([0,2 \pi]\). In addition, they give some error expressions and some convergence results.