Orthogonal polynomials with periodically modulated recurrence coefficients in the Jordan block case

Abstract

We study orthogonal polynomials with periodically modulated recurrence coefficients when $0$ lies on the hard edge of the spectrum of the corresponding periodic Jacobi matrix. In particular, we show that their orthogonality measure is purely absolutely continuous on a real half-line and purely discrete on its complement. Additionally, we provide the constructive formula for the density in terms of Turán determinants. Moreover, we determine the exact asymptotic behavior of the orthogonal polynomials. Finally, we study scaling limits of the Christoffel-Darboux kernel.

56 pages, 1 figure. It will appear at Annales de l'Institut Fourier

References in corpus (4)

• Orthogonal polynomial ensembles in probability theory
• Spectral analysis of a class of hermitian Jacobi matrices in a critical (double root) hyperbolic case
• An example of spectral phase transition phenomenon in a class of Jacobi matrices with periodically modulated weights
• Asymptotic behavior of orthogonal polynomials. Singular critical case

Cited by in corpus (3)

• Asymptotic zeros' distribution of orthogonal polynomials with unbounded recurrence coefficients
• Sturm-Liouville operators with periodically modulated parameters. Part I: Regular case
• Nevai's condition for measures with unbounded supports