Abstract
This chapter covers fundamental results on the spectral theory, including Fredholm alternative theorem and Nussbaum’s theorem on the radius of essential spectrum for bounded linear operators; growth bound and essential growth bound of linear operators; the relationship between the spectrum of semigroups and the spectrum of their infinitesimal generators; spectral decomposition of the state space; and asynchronous exponential growth of linear operators. The estimates of growth bound and essential growth bound of linear operators will be used in proving the center manifold theorem in Chapter 6
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Magal, P., Ruan, S. (2018). Spectral Theory for Linear Operators. In: Theory and Applications of Abstract Semilinear Cauchy Problems. Applied Mathematical Sciences, vol 201. Springer, Cham. https://doi.org/10.1007/978-3-030-01506-0_4
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