A note on the dichotomy spectrum

DOI10.1080/10236190802320147zbMath1180.39030OpenAlexW3017437381MaRDI QIDQ5897006

Christian Poetzsche

Publication date: 18 September 2009

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

Full work available at URL: https://doi.org/10.1080/10236190802320147

zbMATH Keywords

invarianceperturbationsequence spacesexponential dichotomyBanach spacebounded linear operatorsdichotomy spectrumnonautonomous difference equationdichotomy resolvent

Mathematics Subject Classification ID

Spectrum, resolvent (47A10) Perturbation theory of linear operators (47A55) Difference operators (39A70) Linear difference operators (47B39) Spectral sets of linear operators (47A25)

Related Items (13)

Continuity and invariance of the Sacker-Sell spectrum ⋮ Uniform convergence of Nyström discretization on Hölder spaces ⋮ Fredholm theory of families of discrete dynamical systems and its applications to bifurcation theory ⋮ Nonuniform \(\mu \)-dichotomy spectrum and kinematic similarity ⋮ Fine structure of the dichotomy spectrum ⋮ Nonuniform dichotomy spectrum and reducibility for nonautonomous difference equations ⋮ A new metric yielding a richer class of unbounded functions having compact hulls in the shift flow ⋮ Dichotomy spectra of triangular equations ⋮ A note on the dichotomy spectrum ⋮ Uniformly exponential Dichotomy for strongly continuous quasi groups ⋮ A new method to prove the nonuniform dichotomy spectrum theorem in ℝⁿ ⋮ NONUNIFORM DICHOTOMY SPECTRUM INTERVALS: THEOREM AND COMPUTATION ⋮ Nonuniform dichotomy spectrum and reducibility for nonautonomous equations

Cites Work

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• The splitting index for linear differential systems
• Dichotomy, discrete Bohl exponents, and spectrum of block weighted shifts
• A spectral theory for linear differential systems
• The concept of spectral dichotomy for linear difference equations
• Asymptotic behavior of recursions via fixed point theory
• The dichotomy spectrum for noninvertible systems of linear difference equations
• The concept of spectral dichotomy for linear difference equations II

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