Two Universality Results for Polynomial Reproducing Kernels

Abstract

We prove two new universality results for polynomial reproducing kernels of compactly supported measures. The first applies to measures on the unit circle with a jump and a singularity in the weight at $1$ and the second applies to area-type measures on a certain disconnected polynomial lemniscate. In both cases, we apply methods developed by Lubinsky to obtain our results.

21 pages, 1 figure. Version 2 incorporates new references that shorten and simplify the proofs in Section 2. Other minor typos are corrected