Abstract
The purpose of this chapter is to study the strongly continuous semiflow of bounded operators defined by abstract linear functional differential equations. Of main interest are the infinitesimal generators, their spectral properties, the distribution of characteristic values, the decomposition of state spaces according to characteristic values, and the computation of center subspaces. These results will be applied in later chapters to establish stable, unstable, and center manifold theory as well as the Hopf bifurcation theory for nonlinear systems.
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© 1996 Springer-Verlag New York, Inc.
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Wu, J. (1996). Generators and Decomposition of State Spaces for Linear Systems. In: Theory and Applications of Partial Functional Differential Equations. Applied Mathematical Sciences, vol 119. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4050-1_4
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DOI: https://doi.org/10.1007/978-1-4612-4050-1_4
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-8479-6
Online ISBN: 978-1-4612-4050-1
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