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# Applications of universality limits to zeros and reproducing kernels of orthogonal polynomials

@article{Levin2008ApplicationsOU, title={Applications of universality limits to zeros and reproducing kernels of orthogonal polynomials}, author={Eli Levin and Doron S. Lubinsky}, journal={Journal of Approximation Theory}, year={2008}, volume={150}, pages={69-95} }

- Published 2008 in Journal of Approximation Theory
DOI:10.1016/j.jat.2007.05.003

We apply universality limits to asymptotics of spacing of zeros fxkng of orthogonal polynomials, for weights with compact support and for exponential weights. A typical result is lim n!1 xkn xk+1;n ~ Kn (xkn; xkn) = 1 under minimal hypotheses on the weight, with ~ Kn denoting a normalized reproducing kernel. Moreover, for exponential weights, we derive asymptotics for the di¤erentiated kernels K (r;s) n (x; x) = n 1 X k=0 p (r) k (x) p (s) k (x) : 1. Introduction and Results Let be a
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