Universality limits involving orthogonal polynomials on a smooth closed contour

Eli Levin, Doron S. Lubinsky

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


We establish universality limits for measures on a smooth closed contour Γ in the plane. Assume that μ is a regular measure on Γ, in the sense of Stahl, Totik, and Ullmann. Let Γ1 be a closed subarc of Γ, such that μ is absolutely continuous in an open arc containing Γ1, and μ is positive and continuous in that open subarc. Then universality for μ holds in Γ1, in the sense that the reproducing kernels (Kn (z, t)) for μ satisfy (Formula Presented) uniformly for z0 ∈ Γ1, and s, t in compact subsets of the complex plane. Here (Formula Presented) is the sinc kernel, and ф is a conformal map of the exterior of Γ onto the exterior of the unit ball.

Original languageEnglish
Title of host publicationContemporary Mathematics
PublisherAmerican Mathematical Society
Number of pages11
StatePublished - 2016

Publication series

NameContemporary Mathematics
ISSN (Print)0271-4132
ISSN (Electronic)1098-3627

Bibliographical note

Publisher Copyright:
© 2016 E. Levin, D. S. Lubinsky.


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