Asymptotics of orthogonal polynomials with slowly oscillating recurrence coefficients

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.

32 pages

References in corpus (2)

• Asymptotic behaviour of Christoffel-Darboux kernel via three-term recurrence relation II
• Chromatic Derivatives, Chromatic Expansions and Associated Spaces

Cited by in corpus (12)

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• Asymptotic behaviour of Christoffel-Darboux kernel via three-term recurrence relation II
• Asymptotic behaviour of Christoffel-Darboux kernel via three-term recurrence relation I
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• Orthogonal polynomials with periodically modulated recurrence coefficients in the Jordan block case II
• Spectral properties of some complex Jacobi matrices
• Orthogonal polynomials with periodically modulated recurrence coefficients in the Jordan block case
• Asymptotic zeros' distribution of orthogonal polynomials with unbounded recurrence coefficients
• Asymptotic behavior of orthogonal polynomials. Singular critical case
• Universality for random matrices with equi-spaced external source: a case study of a biorthogonal ensemble
• Nevai's condition for measures with unbounded supports
• Sturm-Liouville operators with periodically modulated parameters. Part I: Regular case