A discrete Levinson theorem for systems with singular limit and estimates of generalized eigenvectors of some Jacobi operators

DOI10.1080/10236198.2012.738676zbMath1295.39011OpenAlexW2005100235MaRDI QIDQ2846804

Marcin Moszyński

Publication date: 3 September 2013

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

Full work available at URL: https://doi.org/10.1080/10236198.2012.738676

zbMATH Keywords

eigenvalueJacobi matricesasymptotic behavior of solutionsgeneralized eigenvectorsLevinson-type theoremlinear systems of difference equationsdiscrete and point spectrumlinear recursion systemspectral analysis of Jacobi operators

Mathematics Subject Classification ID

Discrete-time control/observation systems (93C55) Spectrum, resolvent (47A10) Jacobi (tridiagonal) operators (matrices) and generalizations (47B36) Growth, boundedness, comparison of solutions to difference equations (39A22) Linear difference equations (39A06)

Related Items (1)

Spectral results for perturbed periodic Jacobi matrices using the discrete Levinson technique

Cites Work

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• A generalization of Poincaré's theorem for recurrence equations
• Decomposition of matrix sequences
• Trace class perturbations and the absence of absolutely continuous spectra
• Spectral properties of Jacobi matrices by asymptotic analysis.
• Spectral properties of some Jacobi matrices with double weights.
• Unbounded Jacobi Matrices with Empty Absolutely Continuous Spectrum
• Uniform and Smooth Benzaid-Lutz Type Theorems and Applications to Jacobi Matrices
• Slowly oscillating perturbations of periodic Jacobi operators in l²(N)
• Asymptotic Representation of Solutions of Perturbed Systems of Linear Difference Equations
• New discrete Levinson type asymptotics of solutions of linear systems

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