Sieved para-orthogonal polynomials on the unit circle

Sieved orthogonal polynomials on the unit circle were introduced independently by Ismail and Li (1992) [15] and Marcellán and Sansigre (1991) [19]. We look at the para-orthogonal polynomials, chain sequences and quadrature formulas that follow from the kernel polynomials of sieved orthogonal polynomials on the unit circle.