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.
|Title of host publication||Contemporary Mathematics|
|Publisher||American Mathematical Society|
|Number of pages||11|
|State||Published - 2016|
Bibliographical notePublisher Copyright:
© 2016 E. Levin, D. S. Lubinsky.