Abstract
In this chapter we describe the basic notions of a linear C 0-semigroup and the related concepts of an infinitesimal generator. These concepts form infinite dimensional versions of solutions of the finite dimensional linear ordinary differential equation ə t x = Ax.In particular, the C 0-semigroup corresponds to the solution operator or the fundamental solution matrix, and the infinitesimal generator corresponds to the linear coefficient matrix A. We will see that the C 0-semigroups are linear prototypes of the semiflows described in Chapter 2.
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Sell, G.R., You, Y. (2002). Linear Semigroups. In: Dynamics of Evolutionary Equations. Applied Mathematical Sciences, vol 143. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-5037-9_3
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DOI: https://doi.org/10.1007/978-1-4757-5037-9_3
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-3118-4
Online ISBN: 978-1-4757-5037-9
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