Asymptotics of orthogonal polynomials with slowly oscillating recurrence coefficients

2019/02/06 by Grzegorz Świderski, Bartosz Trojan · 17 citations
Mathematics · #Algebraic and Geometric Analysis #Classical orthogonal polynomials #Mathematical analysis #Mathematical functions and polynomials #Mathematics #Orthogonal polynomials #Pure mathematics #Recurrence relation #Spectral Theory in Mathematical Physics #math.CA #math.SP #msc:42C05 #msc:47B36

paper · pdf · doi:10.1016/j.jfa.2019.108326

published in Journal of Functional Analysis 278(3), 108326 (Elsevier BV) · 32 pages

arxiv created 2019/02/06 · openalex publication_date 2019/09/25 · openalex created_date 2019/10/03 · arxiv updated 2020/03/05 · openalex updated_date 2026/08/05

Abstract

We study solutions of three-term recurrence relations whose N-step transfer matrices belong to the uniform Stolz class. In particular, we derive the first order of their uniform asymptotics. For orthonormal polynomials we show more. Namely, we find the constructive formula for the density of their orthogonality measure in terms of Turán determinants and we determine their exact asymptotic behavior. We treat both bounded and unbounded cases in a uniform manner.

Citations

• Chromatic Derivatives, Chromatic Expansions and Associated Spaces
• Operators with Singular Continuous Spectrum: I. General Operators
• Periodic perturbations of unbounded Jacobi matrices II: Formulas for density