## Abstract

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 Γ_{1} be a closed subarc of Γ, such that μ is absolutely continuous in an open arc containing Γ_{1}, and μ^{′} is positive and continuous in that open subarc. Then universality for μ holds in Γ_{1}, in the sense that the reproducing kernels (K_{n} (z, t)) for μ satisfy (Formula Presented) uniformly for z_{0} ∈ Γ_{1}, 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 language | English |
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Title of host publication | Contemporary Mathematics |

Publisher | American Mathematical Society |

Pages | 187-197 |

Number of pages | 11 |

DOIs | |

State | Published - 2016 |

### Publication series

Name | Contemporary Mathematics |
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Volume | 667 |

ISSN (Print) | 0271-4132 |

ISSN (Electronic) | 1098-3627 |

### Bibliographical note

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