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}
}
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 …nite… CONTINUE READING
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