Uniform continuity and compactness for resolvent families of operators

DOI10.1007/BF00992842zbMath0842.45009MaRDI QIDQ1897266

Carlos Lizama

Publication date: 24 July 1996

Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)

zbMATH Keywords

semigroup of operatorscompactnessBanach spaceuniform continuityresolvent familycosine-families of operatorsVolterra convolution equation

Mathematics Subject Classification ID

Other nonlinear integral equations (45G10) One-parameter semigroups and linear evolution equations (47D06) Operator sine and cosine functions and higher-order Cauchy problems (47D09) Abstract integral equations, integral equations in abstract spaces (45N05)

Related Items (4)

Ergodicity and stability for \((b, l)\)-regularized resolvent operator families ⋮ On Volterra Equations Associated with a Linear Operator ⋮ Resolvent norm decay does not characterize norm continuity ⋮ Multiplicative perturbations ofC-regularized resolvent families

Cites Work

• A characterization of periodic resolvent operators
• On the correctness of the problem of inverting the finite Hilbert transform in certain aeroelastic models
• Semigroups of linear operators and applications to partial differential equations
• On linear Volterra equations in Banach spaces
• Cosine operator families such that C(t)-I is compact, for all \(t>0\)
• One-parameter semigroups of positive operators
• Uniform convergence of operators on \(L^{\infty}\) and similar spaces
• A generalization of the Vidav-Jörgens perturbation theorem for semigroups and its application to transport theory
• Linear integro-differential equations in Banach spaces
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