Generators and Decomposition of State Spaces for Linear Systems
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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.
KeywordsState Space Functional Differential Equation Essential Spectrum Negative Real Part Infinitesimal Generator
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