Periodic perturbations of unbounded Jacobi matrices II: Formulas for density

2016/02/29 by Grzegorz Świderski · 4 citations
Computer Science · Mathematics · #Mathematical functions and polynomials #Matrix Theory and Algorithms #Spectral Theory in Mathematical Physics #math.CA #math.SP #msc:42C05

paper · pdf · doi:10.1016/j.jat.2017.01.004

published as Journal of Approximation Theory 216, 67-85 (2017) · 21 pages, 2 figures, 2 tables

arxiv created 2016/11/07 · arxiv updated 2017/02/07

Abstract

We give formulas for the density of the measure of orthogonality for orthonormal polynomials with unbounded recurrence coefficients. The formulas involve limits of appropriately scaled Turán determinants or Christoffel functions. Exact asymptotics of the polynomials and numerical examples are also provided.

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