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dc.contributor.authorLatushkin, Yuri, 1956-eng
dc.contributor.authorMontgomery-Smith, Stephen, 1963-eng
dc.descriptionThe final version of this paper appears in: "Journal of Differential Equations" 125 (1996): 73-116. Print.eng
dc.description.abstractWe study evolutionary semigroups generated by a strongly continuous semi-cocycle over a locally compact metric space acting on Banach fibers. This setting simultaneously covers evolutionary semigroups arising from nonautonomuous abstract Cauchy problems and C0-semigroups, and linear skew-product flows. The spectral mapping theorem for these semigroups is proved. The hyperbolicity of the semigroup is related to the exponential dichotomy of the corresponding linear skew-product flow. To this end a Banach algebra of weighted composition operators is studied. The results are applied in the study of: "roughness" of the dichotomy, dichotomy and solutions of nonhomogeneous equations, Green's function for a linear skew-product flow, "pointwise" dichotomy versus "global" dichotomy, and evolutionary semigroups along trajectories of the flow.eng
dc.relation.ispartofMathematics publications (MU)eng
dc.relation.ispartofcommunityUniversity of Missouri-Columbia. College of Arts and Sciences. Department of Mathematicseng
dc.subjectExponential dichotomyeng
dc.subject.lcshBanach spaceseng
dc.titleEvolutionary semigroups and Lyapunov theorems in Banach spaceseng

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