On the Finiteness of the Number of Eigenvalues of Jacobi Operators below the Essential Spectrum

DOI10.1080/10236190310001641227zbMath1049.39027arXivmath/0109213OpenAlexW3106065854WikidataQ57343946 ScholiaQ57343946MaRDI QIDQ4471235

Gerald Teschl, Franz Luef

Publication date: 18 June 2004

Published in: Journal of Difference Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0109213

zbMATH Keywords

eigenvaluespositive solutionspectral theoryessential spectrumSturm-Liouville operatorsJacobi operatorKneser's theoremdiscrete oscillation theory

Mathematics Subject Classification ID

Sturm-Liouville theory (34B24) General spectral theory of ordinary differential operators (34L05) Discrete version of topics in analysis (39A12) Difference operators (39A70)

Related Items (8)

Oscillation constants for half-linear difference equations with coefficients having mean values ⋮ Expansion of eigenvalues of the perturbed discrete bilaplacian ⋮ Critical oscillation constant for difference equations with almost periodic coefficients ⋮ Oscillation criteria for second-order nonlinear difference equations of Euler type ⋮ Linearized Riccati technique and (non-)oscillation criteria for half-linear difference equations ⋮ Oscillation and nonoscillation of asymptotically almost periodic half-linear difference equations ⋮ Bound states of discrete Schrödinger operators with super-critical inverse square potentials ⋮ Threshold analysis of the one-rank perturbation non-local discrete Laplacian

Cites Work

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• On the spectra of infinite-dimensional Jacobi matrices
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• Spectral analysis of second order difference equations
• Oscillation theory and renormalized oscillation theory for Jacobi operators
• Oscillatory Second Order Linear Difference Equations and Riccati Equations
• Growth, Oscillation and Comparison Theorems for Second Order Linear Difference Equations
• An upper bound on the number of eigenvalues of an infinite dimensional Jacobi matrix
• Growth and Oscillation Properties of Second Order Linear Difference Equations
• Perturbative Oscillation Criteria and Hardy-Type Ineqalities

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