© 2006

A Short Course on Operator Semigroups

  • Special feature -- treatment of spectral theory leading to a detailed qualitative theory for semigroups

  • Concise introduction providing modern tools for the study of linear evolution equations

  • Exercises at the end of chapters

  • High quality and careful exposition


Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-x
  2. Pages 1-33
  3. Pages 205-221
  4. Back Matter
    Pages 222-248

About this book


The book gives a streamlined and systematic introduction to strongly continuous semigroups of bounded linear operators on Banach spaces. It treats the fundamental Hille-Yosida generation theorem as well as perturbation and approximation theorems for generators and semigroups. The special feature is its treatment of spectral theory leading to a detailed qualitative theory for these semigroups. This theory provides a very efficient tool for the study of linear evolution equations arising as partial differential equations, functional differential equations, stochastic differential equations, and others. Therefore, the book is intended for those wanting to learn and apply functional analytic methods to linear time dependent problems arising in theoretical and numerical analysis, stochastics, physics, biology, and other sciences. It should be of interest to graduate students and researchers in these fields.


banach spaces differential equation dynamical systems mathematical analysis operator perturbation perturbation theory spectral theory

Authors and affiliations

  1. 1.Faculty of EngineeringDivision of MathematicsMonteluco di Roio (AQ)Italy
  2. 2.Mathematics InstituteTübingen UniversityTübingenGermany

Bibliographic information

  • Book Title A Short Course on Operator Semigroups
  • Authors Klaus-Jochen Engel
    Rainer Nagel
  • Series Title Universitext
  • DOI
  • Copyright Information Springer Science+Business Media, LLC. 2006
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-0-387-31341-2
  • Softcover ISBN 978-1-4419-2174-1
  • eBook ISBN 978-0-387-36619-7
  • Edition Number 1
  • Number of Pages X, 248
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Operator Theory
  • Buy this book on publisher's site


"The previous book by these authors \ref[ One-parameter semigroups for linear evolution equations, Springer, New York, 2000; MR1721989 (2000i:47075)] in a short time has become an indispensable tool for graduate students and researchers working in the area of evolution equations. However, the sheer amount of information in that book often has made it difficult to navigate and find necessary information and, possibly, has discouraged beginners attempting to enter the field. The volume under review is, to a large extent, a streamlined version of the earlier book and is limited to topics which are essential to making first steps into the world of semigroups. In many cases the results are presented in a weaker version with modified, easier proofs. However, as the authors mention in the Preface, "to a large extent this book consists of excerpts taken from our graduate text"....Nevertheless, I thoroughly enjoyed reading this book and, in my opinion, it should have a necessary position on the bookshelf of any analyst working in operator theory and evolution equations."   (Jacek Banasiak, Mathematical Reviews)