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Semigroups of Linear Operators: With Applications to Analysis, Probability and Physics

Semigroups of Linear Operators: With Applications to Analysis, Probability and Physics

Semigroups of Linear Operators: With Applications to Analysis, Probability and Physics Paperback / softback -

by David Applebaum

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Paperback / softback. New. The theory of semigroups of operators is a topic with great intellectual beauty and wide-ranging applications. This graduate-level introduction presents the essential elements of the theory, introducing the key notions and establishing the central theorems. A mixture of applications are included and further development directions are indicated.
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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.

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Citations

  • Choice, 04/01/2020, Page 0
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