On sieved orthogonal polynomials. IX: Orthogonality on the unit circle

Mourad Ismail and Xin Li

Vol. 153 (1992), No. 2, 289–297

DOI: 10.2140/pjm.1992.153.289

Abstract

We study sieved orthogonal polynomials on the unit circle and using a result of Szegö we show that there is a one to one correspondence between a family of sieved orthogonal polynomials on the unit circle and two families of sieved orthogonal polynomials on the interval [−1,1], namely sieved polynomials of the first and second kinds. We find explicit representations of the sieved polynomials and the Herglotz transform of the measure with respect to which they are orthogonal.

Mathematical Subject Classification 2000

Primary: 42C05

Secondary: 33C45

Milestones

Received: 17 October 1990

Revised: 15 February 1991

Published: 1 April 1992