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 ${\alpha }_n={\sum }_{\ell =1}^L{C}_{\ell }{b}_{\ell }^n+O((b\Delta {)}^n)$ where $\Delta <1$ and $\abs{b_\ell} = b<1$.

Keywords: orthogonal polynomials, Jacobi matrices, CMV matrices

References in corpus (1)

• Fine Structure of the Zeros of Orthogonal Polynomials, I. A Tale of Two Pictures

Cited by in corpus (3)

• Szego polynomials: a view from the Riemann-Hilbert window
• Meromorphic Szego functions and asymptotic series for Verblunsky coefficients
• Fine structure of the zeros of orthogonal polynomials, III. Periodic recursion coefficients