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

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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.
Keywords: orthogonal polynomials, Jacobi matrices, CMV matrices

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Spectral Theory, Primary 4C05 ; Secondary 47B36, 42C05

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http://salesiana.dossiersoluciones.com/handle/123456789/73272

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0411391
 http://arxiv.org/abs/math/0411391

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arXiv