On the convergence and approximation of cosine functions

DOI10.1007/BF01832857zbMath0282.47012OpenAlexW4243746811MaRDI QIDQ1843954

Jerome A. Goldstein

Publication date: 1974

Published in: Aequationes Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/136414

Mathematics Subject Classification ID

Groups and semigroups of linear operators (47D03) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65) General theory of functional equations and inequalities (39B05) Groups and semigroups of linear operators, their generalizations and applications (47D99)

Related Items (16)

Fractional measure-dependent nonlinear second-order stochastic evolution equations with Poisson jumps ⋮ Abstract Volterra Integro-Differential Equations: Approximation and Convergence of Resolvent Operator Families ⋮ Abstract functional second-order stochastic evolution equations with applications ⋮ Goldstein-Wentzell boundary conditions: recent results with Jerry and Gisèle Goldstein ⋮ A representation formula for strongly continuous cosine families ⋮ Some developments in semigroups of operators since Hille-Phillips ⋮ Cosine families and semigroups really differ ⋮ Approximations of Laplace transforms and integrated semigroups ⋮ A class of second-order McKean-Vlasov stochastic evolution equations driven by fractional Brownian motion and Poisson jumps ⋮ Approximation theorems for the propagators of higher order abstract Cauchy problems ⋮ An approximation of solutions to heat equations defined by generalized measure theoretic Laplacians ⋮ On approximation and representation of \(k\)-regularized resolvent families ⋮ Unnamed Item ⋮ Cosine families and abstract nonlinear second order differential equations ⋮ Convergence of solutions of a second order Cauchy problem ⋮ Functionals-preserving cosine families generated by Laplace operators in \(C[0,1\)]

Cites Work

• Unnamed Item
• Ordinary differential equations in linear topological spaces. I
• Ordinary differential equations in linear topological space. II
• On operator ranges
• Approximation of nonlinear semigroups and evolution equations
• Some counterexamples involving selfadjoint operators
• A proof of the Trotter-Kato theorem on approximation of semi-groups

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