Asymptotic zero distribution of orthogonal polynomials with discontinuously varying recurrence coefficients

The zero distribution of orthogonal polynomials p(n, N), n = 0, 1, ... gene rated by recurrence coefficients a(n,N) and b(n, N) depending on it paramet er N has been recently considered by Kuijlaars and Van Assche under the ass umption that a(n, N) and b(n, N) behave like a(n/N) and b(n/N), respectivel y, where a((.)) and b((.)) are continuous functions. Here, we extend this r esult by allowing a((.)) and b((.)) to be measurable functions so that the presence of possible jumps is included. The novelty is also in the sense of the mathematical tools since, instead of applying complex analysis argumen ts, we use recently developed results from asymptotic matrix theory due to Tyrtyshnikov, Serra Capizzano, and Tilli. (C) 2001 Academic Press.