Weak convergence of CD kernels and applications

Abstract

We prove a general result on equality of the weak limits of the zero counting measure, dνn, of orthogonal polynomials (defined by a measure dμ) and (1/n)Kn(x,x)dμ(x). By combining this with the asymptotic upper bounds of Máté and Nevai [16] and Totik [33] on nλn(x), we prove some general results on ∫I(1/n)Kn(x,x)dμs→0 for the singular part of dμ and ∫I|ρE(x)−(w(x)/n)Kn(x,x)|dx→0, where ρE is the density of the equilibrium measure and w(x) the density of dμ

Locations

• Duke Mathematical Journal - View
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