A note on fractional derivatives of semigroups and cosine functions

DOI10.2140/pjm.1983.109.335zbMath0495.47026OpenAlexW2031599976MaRDI QIDQ1169667

Hector O. Fattorini

Publication date: 1983

Published in: Pacific Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2140/pjm.1983.109.335

zbMATH Keywords

fractional derivativesstrongly continuous semigroupinfinitesimal generatorabstract differential equationdegree of approximationcosine functions

Mathematics Subject Classification ID

Groups and semigroups of linear operators (47D03) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65) Linear differential equations in abstract spaces (34G10)

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Criterion for the solvability of the Cauchy problem for an abstract Euler-Poisson-Darboux equation ⋮ Perturbation and comparison of cosine operator functions ⋮ Criterion for the solvability of the weighted Cauchy problem for an abstract Euler-Poisson-Darboux equation ⋮ Representation of complex powers of C-sectorial operators ⋮ Characterizations of domains of fractional powers for non-negative operators ⋮ Cosine and sine families on time scales and abstract second order dynamic equations on time scales ⋮ Operator sine functions and exponential trigonometric pairs ⋮ Transmutation Operators as a Solvability Concept of Abstract Singular Equations ⋮ Regularity theory of hyperbolic equations with non-homogeneous Neumann boundary conditions. II: General boundary data ⋮ Semigroups of operators, cosine operator functions, and linear differential equations ⋮ On \(L^p\)-contractivity of semigroups generated by linear partial differential operators

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