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Published in:
2020 | OriginalPaper | Chapter
3. Classes of Semigroups
Authors : Ruth Curtain, Hans Zwart
Published in: Introduction to Infinite-Dimensional Systems Theory
Publisher: Springer New York
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Abstract
The general concept of strongly continuous semigroup was introduced in the previous chapter. In this chapter we focus on examples. This is done by studying three main classes, namely spatially invariant operators, Riesz-spectral operators, and delay equations. Next to existence of the strongly continuous semigroup, we study for these classes the resolvent set and operator, and characterise the semigroup invariant subspaces. The chapter ends with a set of 25 exercises and a notes and references section.