Asymptotic behavior of 𝐶₀-semigroups in Banach spaces

DOI10.1090/S0002-9939-96-03373-4zbMath0863.47027OpenAlexW2167143613MaRDI QIDQ3837602

Lutz W. Weis, Volker Wrobel

Publication date: 10 December 1996

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

Full work available at URL: https://doi.org/10.1090/s0002-9939-96-03373-4

zbMATH Keywords

Cauchy problemsoptimal estimatesasymptotic behavior of strongly continuous semigroupsgrowth abscissas of the resolvent functionLyapunov's classical stability condition

Mathematics Subject Classification ID

One-parameter semigroups and linear evolution equations (47D06)

Related Items (16)

On individual stability of $C_0-$semigroups ⋮ On eventual compactness of collisionless kinetic semigroups with velocities bounded away from zero ⋮ Optimal individual stability estimates for $C_0$-semigroups in Banach spaces ⋮ Asymptotic behaviour of \(C_0\)-semigroups and \(\gamma\)-boundedness of the resolvent ⋮ Individual stability of \(C_0\)-semigroups with uniformly bounded local resolvent ⋮ A weak integral condition and its connections with existence and uniqueness of solutions for some abstract Cauchy problems in Banach spaces ⋮ Exponential stability and uniform boundedness of solutions for nonautonomous periodic abstract Cauchy problems. An evolution semigroup approach ⋮ Sharp growth rates for semigroups using resolvent bounds ⋮ Extensions of the vector-valued Hausdorff-Young inequalities ⋮ New thoughts on the vector-valued Mihlin–Hörmander multiplier theorem ⋮ Stability theory for semigroups using \((L^{p},L^{q})\) Fourier multipliers ⋮ Unnamed Item ⋮ \(B\)-convexity, the analytic Radon-Nikodým property, and individual stability of \(C_0\)-semigroups ⋮ Growth of orbits for operator semigroups on Banach spaces with Schauder bases ⋮ Regularization and frequency-domain stability of well-posed systems ⋮ Operator-valued \((L^p, L^q)\) Fourier multipliers and stability theory for evolution equations

Cites Work

• The resolvent growth assumption for semigroups on Hilbert spaces
• Semigroups of linear operators and applications to partial differential equations
• On the asymptotic behaviour of a semigroup of linear operators
• Sur la transformation de Fourier des fonctions à valeurs vectorielles
• Spectral Theory for Contraction Semigroups on Hilbert Space
• The Stability of Positive Semigroups on L p Spaces
• Fractional powers of operators
• Unnamed Item
• Unnamed Item

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