# Topics in Operator Semigroups

- 6 Citations
- 6.8k Downloads

Part of the Progress in Mathematics book series (PM, volume 281)

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- 6 Citations
- 6.8k Downloads

Part of the Progress in Mathematics book series (PM, volume 281)

The theory of operator semigroups was essentially discovered in the early 1930s. Since then, the theory has developed into a rich and exciting area of functional analysis and has been applied to various mathematical topics such as Markov processes, the abstract Cauchy problem, evolution equations, and mathematical physics.

This self-contained monograph focuses primarily on the theoretical connection between the theory of operator semigroups and spectral theory. Divided into three parts with a total of twelve distinct chapters, this book gives an in-depth account of the subject with numerous examples, detailed proofs, and a brief look at a few applications.

Topics include:

* The Hille–Yosida and Lumer–Phillips characterizations of semigroup generators

* The Trotter–Kato approximation theorem

* Kato’s unified treatment of the exponential formula and the Trotter product formula

* The Hille–Phillips perturbation theorem, and Stone’s representation of unitary semigroups

* Generalizations of spectral theory’s connection to operator semigroups

* A natural generalization of Stone’s spectral integral representation to a Banach space setting

With a collection of miscellaneous exercises at the end of the book and an introductory chapter examining the basic theory involved, this monograph is suitable for second-year graduate students interested in operator semigroups.

Nussbaum’s theorem Stone’s representation Trotter product formula Trotter--Kato approximation theorem functional analysis operator semigroups spectral theory unitary semigroups

- DOI https://doi.org/10.1007/978-0-8176-4932-6
- Copyright Information Birkhäuser Boston 2010
- Publisher Name Birkhäuser Boston
- eBook Packages Mathematics and Statistics
- Print ISBN 978-0-8176-4931-9
- Online ISBN 978-0-8176-4932-6
- Series Print ISSN 0743-1643
- Series Online ISSN 2296-505X
- Buy this book on publisher's site