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

DOI10.1016/j.jat.2017.01.003zbMath1367.47040arXiv1602.06273OpenAlexW2340022662MaRDI QIDQ514217

Grzegorz Świderski, Bartosz Trojan

Publication date: 28 February 2017

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1602.06273

zbMATH Keywords

total variationJacobi matrixasymptotics of generalized eigenvectors

Mathematics Subject Classification ID

Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Perturbation theory of linear operators (47A55) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80) Jacobi (tridiagonal) operators (matrices) and generalizations (47B36)

Related Items (9)

Spectral properties of block Jacobi matrices ⋮ About essential spectra of unbounded Jacobi matrices ⋮ Periodic perturbations of unbounded Jacobi matrices III: the soft edge regime ⋮ Uni-asymptotic linear systems and Jacobi operators ⋮ Orthogonal polynomials with periodically modulated recurrence coefficients in the Jordan block case. II ⋮ Periodic perturbations of unbounded Jacobi matrices. II: Formulas for density. ⋮ Titchmarsh-Weyl formula for the spectral density of a class of Jacobi matrices in the critical case ⋮ Asymptotics of orthogonal polynomials with slowly oscillating recurrence coefficients ⋮ Spectral properties of some complex Jacobi matrices

Cites Work

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• Periodic perturbations of unbounded Jacobi matrices. II: Formulas for density.
• Spectral properties of unbounded Jacobi matrices with almost monotonic weights
• Spectral theory for a class of periodically perturbed unbounded Jacobi matrices: Elementary methods
• Spectral gaps resulting from periodic perturbations of a class of Jacobi operators
• Asymptotic behaviour of some families of orthonormal polynomials and an associated Hilbert space
• Approximating the weight function for orthogonal polynomials on several intervals
• Spectral analysis of second order difference equations
• Strong nonsubordinacy and absolutely continuous spectra for Sturm- Liouville equations
• The classical moment problem as a self-adjoint finite difference operator
• Spectral analysis of selfadjoint Jacobi matrices with periodically modulated entries
• Alternative approaches to the absolute continuity of Jacobi matrices with monotonic weights.
• Spectral properties of Jacobi matrices by asymptotic analysis.
• Spectral properties of some Jacobi matrices with double weights.
• A spectral analysis for self-adjoint operators generated by a class of second order difference equations
• Orthogonal polynomials, spectral measures, and absolute continuity
• On the order of indeterminate moment problems
• Chromatic Derivatives, Chromatic Expansions and Associated Spaces
• Hypergeometric Orthogonal Polynomials and Their q-Analogues
• Orthogonal Polynomials, Measures and Recurrence Relations
• On an Asymptotic Equality for Reproducing Kernels and Sums of Squares of Orthonormal Polynomials
• A Riemann-Hilbert approach to asymptotic questions for orthogonal polynomials

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