Szegö Polynomials: Quadrature Rules on the Unit Circle and on $[-1,1]$

R. Bressan, S.F. Menegasso, A. Sri Ranga
2003 Rocky Mountain Journal of Mathematics  
Dedicated to Professor William B. Jones on the occasion of his 70th birthday ABSTRACT. We consider some of the relations that exist between real Szegö polynomials and certain para-orthogonal polynomials defined on the unit circle, which are again related to certain orthogonal polynomials on [−1, 1] through the transformation x = (z 1/2 +z −1/2 )/2. Using these relations we study the interpolatory quadrature rule based on the zeros of polynomials which are linear combinations of the orthogonal
more » ... lynomials on [−1, 1]. In the case of any symmetric quadrature rule on [−1, 1], its associated quadrature rule on the unit circle is also given.
doi:10.1216/rmjm/1181069967 fatcat:g6jgkhal6zfi7atyjl45i6pafa