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

Barry Simon

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arXiv · math/0411391

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

Barry Simon

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Abstract

Mhaskar-Saff found a kind of universal behavior for the bulk structure of the zeros of orthogonal polynomials for large $n$. Motivated by two plots, we look at the finer structure for the case of random Verblunsky coefficients and for what we call the BLS condition: $α_n = Cb^n + O((bΔ)^n)$. In the former case, we describe results of Stoiciu. In the latter case, we prove asymptotically equal spacing for the bulk of zeros.

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Barry Simon. 2004-11-17. Fine Structure of the Zeros of Orthogonal Polynomials, I. A Tale of Two Pictures. https://arxiv.org/abs/math/0411391

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