Asymptotic behaviour of Christoffel-Darboux kernel via three-term recurrence relation I

Abstract

For Jacobi parameters belonging to one of the three classes: asymptotically periodic, periodically modulated and the blend of these two, we study the asymptotic behavior of the Christoffel functions and the scaling limits of the Christoffel-Darboux kernel. We assume regularity of Jacobi parameters in terms of the Stolz class. We emphasize that the first class only gives rise to measures with compact supports.

47 pages

References in corpus (3)

• Asymptotics of orthogonal polynomials with slowly oscillating recurrence coefficients
• Asymptotic behaviour of Christoffel-Darboux kernel via three-term recurrence relation II
• About essential spectra of unbounded Jacobi matrices

Cited by in corpus (8)

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