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Published in:
2020 | OriginalPaper | Chapter
2. Semigroup Theory
Authors : Ruth Curtain, Hans Zwart
Published in: Introduction to Infinite-Dimensional Systems Theory
Publisher: Springer New York
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Abstract
Strongly continuous semigroups and their infinitesimal generators are treated in detail in this chapter. The chapter contains the classical concepts and results on these topics, such as the Hille-Yosida Theorem and the contraction- and dual semigroups. Although the theory can be extended to Banach spaces, we restrict ourselves to separable Hilbert spaces. The relation between semigroup- and generator-invariant subspaces is studied in detail. The chapter ends with a set of 30 exercises and a notes and references section.