Lyapunov theorems for Banach spaces

DOI10.1090/S0273-0979-1994-00495-1zbMath0815.47052OpenAlexW2062808849MaRDI QIDQ4302527

Yuri Latushkin, Stephen J. Montgomery-Smith

Publication date: 21 August 1994

Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0273-0979-1994-00495-1

zbMATH Keywords

exponential dichotomy for nonautonomous differential equationsgenerator of the semigroup of evolutionary operatorsspectral mapping theorem for semigroups on any Banach space

Mathematics Subject Classification ID

One-parameter semigroups and linear evolution equations (47D06) Stability of solutions to ordinary differential equations (34D20) General theory of ordinary differential operators (47E05) Linear operators on function spaces (general) (47B38) Linear differential equations in abstract spaces (34G10)

Related Items (11)

The spectrum of the kinematic dynamo operator for an ideally conducting fluid ⋮ Dichotomy of differential equations on Banach spaces and an algebra of weighted translation operators ⋮ The spectral mapping theorem for evolution semigroups on spaces of vector-valued functions ⋮ Spectral analysis of abstract parabolic operators in homogeneous function spaces, II ⋮ Nonlinear boundary-value problems for the Lyapunov equation in the space \(L_p\) ⋮ Generalized evolution semigroups and general dichotomies ⋮ Stability and dichotomy of positive semigroups on 𝐿_{𝑝} ⋮ Some applications of Fejer’s theorem to operator cosine functions in Banach spaces ⋮ Spectral analysis of abstract parabolic operators in homogeneous function spaces ⋮ Uniformly exponential Dichotomy for strongly continuous quasi groups ⋮ Autonomous nonlinear boundary-value problems for the Lyapunov equation in the Hilbert space

Cites Work

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• Asymptotic behavior of one-parameter semigroups of positive operators
• Spectral theory for linearizations of dynamical systems
• Analyticity of spectral subbundles
• Hyperbolic evolution semigroups on vector valued function spaces
• Hyperbolic evolution groups and dichotomic evolution families
• Dichotomies for linear evolutionary equations in Banach spaces
• Evolutionary semigroups and Lyapunov theorems in Banach spaces
• Dichotomy of differential equations on Banach spaces and an algebra of weighted translation operators
• Stationary scattering theory for time-dependent Hamiltonians
• Exponential Dichotomies and Fredholm Operators
• Weighted translation operators and linear extensions of dynamical systems

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