A complex Tauberian theorem and mean ergodic semigroups

DOI10.1007/BF02573531zbMath0836.47032OpenAlexW2061139338MaRDI QIDQ1891653

Charles J. K. Batty, Wolfgang Arendt

Publication date: 29 April 1996

Published in: Semigroup Forum (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/135392

zbMATH Keywords

Laplace transformsasymptotic behaviourTauberian theoremsAbel-convergent and Cesàro-convergent functionsergodic \(C_ 0\) semi-groupsinhomogeneous Cauchy problem with periodic inhomogeneity

Mathematics Subject Classification ID

One-parameter semigroups and linear evolution equations (47D06) Functional analytic methods in summability (40H05) Tauberian theorems (40E05)

Related Items (5)

Long time asymptotics for fully nonlinear Bellman equations: a backward SDE approach ⋮ Decay estimates of functions through singular extensions of vector-valued Laplace transforms ⋮ Ergodicity and stability for \((b, l)\)-regularized resolvent operator families ⋮ Rates of approximation and ergodic limits of regularized operator families ⋮ A century of complex Tauberian theory

Cites Work

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• The operator equation \(AX-XB=C\) with unbounded operators \(A\) and \(B\) and related abstract Cauchy problems
• Ergodic theorems. With a supplement by Antoine Brunel
• One-parameter semigroups of positive operators
• Towards a ``Matrix theory for unbounded operator matrices
• On Newman's quick way to the prime number theorem
• Tauberian Theorems for the Laplace-Stieltjes Transform
• Stability of Individual Elements Under One-Parameter Semigroups
• Tauberian Theorems and Stability of One-Parameter Semigroups
• Vector-Valued Tauberian Theorems and Asymptotic Behavior of Linear Volterra Equations
• On Wiener's Method in Tauberian Theorems

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