## Table of contents

## About this book

### Introduction

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.

### Keywords

### Bibliographic information

- 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