A new proof and generalizations of Gearhart’s theorem

DOI10.1090/S0002-9939-07-08691-1zbMath1119.47043OpenAlexW2081817996MaRDI QIDQ3432765

Vu Quoc Phong

Publication date: 18 April 2007

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

Full work available at URL: https://doi.org/10.1090/s0002-9939-07-08691-1

zbMATH Keywords

almost periodic functionsmild solutionsspectral mapping theoremGearhart's theoremadmissible subspace

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) One-parameter semigroups and linear evolution equations (47D06) Applications of operator theory to differential and integral equations (47N20) Linear differential equations in abstract spaces (34G10)

Related Items (5)

Approximations of Parabolic Equations at the Vicinity of Hyperbolic Equilibrium Point ⋮ The exponential dichotomy on general approximation scheme ⋮ On the almost periodic solutions of differential equations on Hilbert spaces ⋮ The exponential dichotomy under discretization on general approximation scheme ⋮ SOLUTION PROPERTIES OF SOME CLASSES OF OPERATOR EQUATIONS IN HILBERT SPACES

Cites Work

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• On a theorem of Gearhart
• The operator equation \(AX-XB=C\), admissibility, and asymptotic behavior of differential equations
• On the Spectrum of C 0 -Semigroups
• Spectral Theory for Contraction Semigroups on Hilbert Space
• SPECTRAL PROPERTIES OF THE OPERATOR EQUATION AX + XB = Y

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