Abstract
Semigroups of linear operators provide the primary tools in the study of continuous-time Markov processes. They arise as the solutions of the initial value problem for the differential equation \(u'(t)=Au(t)\), where A is a linear operator acting on a Banach space. We describe what is generally regarded as the basic theory. We provide basic definitions, examples and theorems characterizing the operators as being the generators of semigroups. The aim here is to provide necessary foundations for studying semigroups on \(L^1\) spaces in the next chapter.
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Rudnicki, R., Tyran-Kamińska, M. (2017). Operator Semigroups. In: Piecewise Deterministic Processes in Biological Models. SpringerBriefs in Applied Sciences and Technology(). Springer, Cham. https://doi.org/10.1007/978-3-319-61295-9_3
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DOI: https://doi.org/10.1007/978-3-319-61295-9_3
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Publisher Name: Springer, Cham
Print ISBN: 978-3-319-61293-5
Online ISBN: 978-3-319-61295-9
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