Table of contents
About this book
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.
* 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.
- 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
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