Asymptotics for orthogonal polynomials and separation of their zeros

Abstract

Let pn denote the orthonormal polynomials associated with a measure μ with compact support on the real line. In a recent paper, we showed there is a close relationship between the spacing of zeros of successive orthogonal polynomials pn,pn−1, and uniform bounds on the orthogonal polynomials in subintervals of the support. In this paper, we show there is also a relationship between asymptotics for the spacing of zeros of pn−1,pn, and pointwise asymptotics for the orthogonal polynomials.