Some results on the asymptotic distribution of the zeros of orthogonal polynomials

摘要

Define a discrete measure that attributes masses of size 1/n at every zero of the polynomial of degree n, orthogonal with respect to some positive measure on the real line. The weak limit of this sequence of measures is studied by many authors. In this paper we give some results on the rate of this asymptotic behaviour, in particular the results show how the behaviour of the spectral measure, with respect to which the polynomials are orthogonal, affects this asymptotic zero behaviour.