Periodic perturbations of unbounded Jacobi matrices II: Formulas for density

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.

arXiv comment21 pages, 2 figures, 2 tables

References in corpus (4)

• The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue
• Periodic perturbations of unbounded Jacobi matrices I: Asymptotics of generalized eigenvectors
• Spectral properties of unbounded Jacobi matrices with almost monotonic weights
• Chromatic Derivatives, Chromatic Expansions and Associated Spaces

Cited by in corpus (15)

• Periodic perturbations of unbounded Jacobi matrices I: Asymptotics of generalized eigenvectors
• Periodic perturbations of unbounded Jacobi matrices III: The soft edge regime
• Asymptotics of orthogonal polynomials with slowly oscillating recurrence coefficients
• About essential spectra of unbounded Jacobi matrices
• Asymptotic behaviour of Christoffel-Darboux kernel via three-term recurrence relation II
• Asymptotic behaviour of Christoffel-Darboux kernel via three-term recurrence relation I
• Spectral properties of block Jacobi matrices
• 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
• Jacobi matrices: continued fractions, approximation, spectrum
• Barrier nonsubordinacy and absolutely continuous spectrum of block Jacobi matrices
• Nevai's condition for measures with unbounded supports
• Spectral density in a Moszynski's class of Jacobi matrices
• Sturm-Liouville operators with periodically modulated parameters. Part I: Regular case