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

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dc.creatorSimon, Barry
dc.date2004-11-17
dc.date.accessioned2026-07-07T05:14:25Z
dc.date.available2026-07-07T05:14:25Z
dc.descriptionMhaskar-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.
dc.descriptionKeywords: orthogonal polynomials, Jacobi matrices, CMV matrices
dc.identifierhttps://arxiv.org/abs/math/0411391
dc.identifierhttp://arxiv.org/abs/math/0411391
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/73272
dc.subjectSpectral Theory
dc.subjectPrimary 4C05 ; Secondary 47B36, 42C05
dc.titleFine Structure of the Zeros of Orthogonal Polynomials, I. A Tale of Two Pictures
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