On Kernel polynomials and self-perturbation of orthogonal polynomials

Abstract

Given an orthogonal polynomial system {Q n (x) } n=0 , define another polynomial system by P n(x) = Q n(x) - α nQ n,(x), n > 0, where α n are complex numbers and t is a positive integer. We find conditions for {P n (x)] n=0 to be an orthogonal polynomial system. When t = 1 and α 1≠ 0, it turns out that {Q n (x) ) n=0 must be kernel polynomials for [P n(x)} n=0 for which we study, in detail, the location of zeros and semi-classical character. ©Springer-Verlag 2001.