Fine Structure of the Zeros of Orthogonal Polynomials, II. OPUC With Competing Exponential Decay

Abstract

We present a complete theory of the asymptotics of the zeros of OPUC with Verblunsky coefficients $α_n = \sum_{\ell=1}^L C_\ell b_\ell^n + O((bΔ)^n)$ where $Δ<1$ and $\abs{b_\ell} = b<1$.

Keywords: orthogonal polynomials, Jacobi matrices, CMV matrices