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

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

2004-11-17

arxiv.org/abs/math/0411392v1

Mathematics

Spectral Theory

Keywords: orthogonal polynomials, Jacobi matrices, CMV matrices

Scientific paper

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 $\abs{b_\ell} = b<1$.

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