Abstract
We 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 non-autonomous 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. © 1996 Academic Press, Inc.
Recommended Citation
Y. Latushkin et al., "Evolutionary Semigroups and Dichotomy of Linear Skew-Product Flows on Locally Compact Spaces with Banach Fibers," Journal of Differential Equations, vol. 125, no. 1, pp. 73 - 116, Elsevier, Feb 1996.
The definitive version is available at https://doi.org/10.1006/jdeq.1996.0025
Department(s)
Mathematics and Statistics
Publication Status
Open Archive
International Standard Serial Number (ISSN)
0022-0396
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2024 Elsevier, All rights reserved.
Publication Date
10 Feb 1996
Comments
National Science Foundation, Grant DMS-9400518