Discrete spectrum in a critical coupling case of Jacobi matrices with spectral phase transitions by uniform asymptotic analysis

DOI10.1016/j.jat.2008.09.005zbMath1182.47030arXiv0803.3288OpenAlexW1998926104MaRDI QIDQ1040873

Luis O. Silva, Serguei Naboko, Irina Pchelintseva

Publication date: 26 November 2009

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

Full work available at URL: https://arxiv.org/abs/0803.3288

zbMATH Keywords

Jacobi matricesdiscrete spectrumuniform asymptoticsRiccati difference equationgeneralised eigenvectorsfirst-order spectral phase transitionmodified Kelley methodPoincaré coefficientsPoincaré type equationsuniform majorant and minorant sequences

Mathematics Subject Classification ID

Spectrum, resolvent (47A10) Jacobi (tridiagonal) operators (matrices) and generalizations (47B36)

Related Items (7)

On the instability of the essential spectrum for block Jacobi matrices ⋮ About essential spectra of unbounded Jacobi matrices ⋮ Periodic perturbations of unbounded Jacobi matrices III: the soft edge regime ⋮ Self-adjoint second-order difference equations with unbounded coefficients in the double root case ⋮ Green matrix estimates of block Jacobi matrices. II: Bounded gap in the essential spectrum ⋮ Orthogonal polynomials with periodically modulated recurrence coefficients in the Jordan block case. II ⋮ Non-existence of subordinate solutions for Jacobi operators in some critical cases

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unbounded Jacobi matrices at critical coupling
• Asymptotic behavior of generalized eigenvectors of Jacobi matrices in the critical (``double root) case
• On subordinacy and analysis of the spectrum of one-dimensional Schrödinger operators
• Asymptotic analysis of solutions in the ``double root case
• Spectral analysis of selfadjoint Jacobi matrices with periodically modulated entries
• Spectral properties of Jacobi matrices by asymptotic analysis.
• Uniform and Smooth Benzaid-Lutz Type Theorems and Applications to Jacobi Matrices
• An Example of Spectral Phase Transition Phenomenon in a Class of Jacobi Matrices with Periodically Modulated Weights
• The asymptotic solution of linear differential systems
• Asymptotic Representation of Solutions of Perturbed Systems of Linear Difference Equations
• The asymptotic analysis of generalized eigenvectors of some Jacobi operators. Jordan box case∗
• On the Nature of the Spectrum of Singular Second Order Linear Differential Equations
• The spectrum of differential operators of order \(2n\) with almost constant coefficients

This page was built for publication: Discrete spectrum in a critical coupling case of Jacobi matrices with spectral phase transitions by uniform asymptotic analysis