Periodic perturbations of unbounded Jacobi matrices I: Asymptotics of generalized eigenvectors

Abstract

We study asymptotics of generalized eigenvectors associated with Jacobi matrices. Under weak conditions on the coefficients we identify when the matrices are self-adjoint and show that they satisfy strong non-subordinacy condition.

34 pages

References in corpus (3)

• Periodic perturbations of unbounded Jacobi matrices II: Formulas for density
• Spectral properties of unbounded Jacobi matrices with almost monotonic weights
• Chromatic Derivatives, Chromatic Expansions and Associated Spaces

Cited by in corpus (12)

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• Periodic perturbations of unbounded Jacobi matrices III: The soft edge regime
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• About essential spectra of unbounded Jacobi matrices
• Asymptotic behaviour of Christoffel-Darboux kernel via three-term recurrence relation II
• Spectral properties of block Jacobi matrices
• 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
• Barrier nonsubordinacy and absolutely continuous spectrum of block Jacobi matrices
• Nevai's condition for measures with unbounded supports