The theory of semigroups of operators is one of the most important
themes in modern analysis. Not only does it have great intellectual
beauty, but also wide-ranging applications. In this book the author
first presents the essential elements of the theory, introducing
the notions of semigroup, generator and resolvent, and establishes
the key theorems of Hille-Yosida and Lumer-Phillips that give
conditions for a linear operator to generate a semigroup. He then
presents a mixture of applications and further developments of the
theory. This includes a description of how semigroups are used to
solve parabolic partial differential equations, applications to
Levy and Feller-Markov processes, Koopmanism in relation to
dynamical systems, quantum dynamical semigroups, and applications
to generalisations of the Riemann-Liouville fractional integral.
Along the way the reader encounters several important ideas in
modern analysis including Sobolev spaces, pseudo-differential
operators and the Nash inequality.
General
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