About semiclassical polynomials on the unit circle corresponding to the class (2,2)

[摘要] In the present paper we pose the problem of characterizing the orthogonal polynomials related to the unit circle whose moment functional L verify a functional relation of the following type D(phi L)+psi L=0, where phi and psi are polynomials with deg phi = 2 and deg psi = 1. Two different situations appear depending on whether the roots of phi are unimodular or not. Here, we solve the last case. Moreover, we analyse the definite positive character of the solutions.

[发布日期] 1997-11-06

[关键词] orthogonal polynomials;unit circle;semiclassical polynomials;regular functionals;measures on the unit circle;difference equations