One-Parameter Semigroups for Linear Evolution Equations

This book gives an up-to-date account of the theory of strongly continuous one-parameter semigroups of linear operators. It includes a systematic discussion of the spectral theory and the long-term behavior of such semigroups. A special feature of the text is an unusually wide range of applications, e.g., to ordinary and partial differential operators, delay and Volterra equations and to control theory, and an emphasis on philosophical motivation and the historical background. The book is written for students, but should also be of value for researchers interested in this field.

List of contents

Contents:
Linear Dynamical Systems
Semigroups, Generators and Resolvents
Perturbation and Approximation of Semigroups. Spectral Theory for Semigroups and Generators
Asymptotics of Semigroups
Semigroups Everywhere
History of the Exponential Function
Appendices

Summary

This book explores the theory of strongly continuous one-parameter semigroups of linear operators. A special feature of the text is an unusually wide range of applications such as to ordinary and partial differential operators, to delay and Volterra equations, and to control theory.

Report

From the reviews:

"This book is a real asset for people who work in the field of operator semigroups, or want to. It is a beauty, not only because it contains so much information, but also because the authors have done everything conceivable to put the whole subject in the right historical and contemporary context." (J. van Casteren, Nieuw Archief voor Wiskunde, Vol. 5/6 (4), 2005)
"This is an excellent introduction to semigroups of operators and applications. ... The book can be recommended primarily to graduate students, but it is also of interest to researchers." (Tibor Krisztin, Acta Scientiarum Mathematicarum, Vol. 69, 2003)
"This book is a continuation of a series of monographs on one-parameter semigroups ... . The book is well written. ... It contains a sufficient number of instructive examples in every chapter. ... Moreover, a lot of exercises are given which may help to understand the abstract theory. Altogether the book can also be used as a good basis for a series of lectures on that topic." (M. Demuth, Jahresberichte der Deutschen Mathematiker Vereinigung, Vol. 104 (1), 2002)
"The present volume can be considered an up-to-date exposition of the theory and applications of linear semigroup theory ... . A detailed history of the exponential function and its connection with semigroup theory gives interesting information ... . A useful appendix is added to help the reader ... . In conclusion, by virtue of its clearness of style and ease of consultation, this book can be recommended to the beginners as well as to the experts in semigroup theory ... ." (Gabriella Di Blasio, Semigroup Forum, Vol. 63 (2), 2001)
"In this book the authors give an excellent presentation of the theory of semigroups ... . The reader can use the text as an introduction ... . At the same time, this book contains many new and very recent results of the theory and its application, thus it is also of great value for experts. ... Notes atthe end of each chapter contain many hints to additional material. Each section ends with a collection of exercises. ... The book turned out very well." (Karl-Heinz Förster, Zentralblatt MATH, Vol. 952, 2001)
"The book offers an introduction to strongly continuous one-parameter semigroups in Banach spaces. ... The book is very well written. Besides the basic text it contains many illustrating examples, exercises and notes. It will certainly be very useful for advanced students and for those mathematicians who want to be acquainted with the most recent results of the field. ... also those who are interested in functional analytic ideas and methods will enjoy reading it." (H. Langer, Internationale Mathematische Nachrichten, Issue 185, 2000)
"This book provides a comprehensive and up-to-date introduction to, and exposition of, the theory of strongly continuous one-parameter semigroups of linear operators and of its applications ... . The book is clearly written, well organized, provides much information and numerous examples ... . Therefore, I can highly recommend this book both to students with a background in basic functional analysis as an introduction into this field, as well as to researchers as a modern and comprehensive exposition of the theory and its applications." (R. Bürger, Monatshefte für Mathematik, Vol. 131 (2), 2000)
"This book is a broad introduction to the theory of C₀-semigroups. ... The steady pace of the text and the very high quality of the exposition make the material in this book easily accessible ... . the book's greatest impact is likely to be through tempting graduate students to learn about semigroups of operators ... . the book should also be of interest to experienced researchers. Most specialists in semigroup theory and applications will be glad to have it ... ." (C. J. K. Batty, Mathematical Reviews, Issue 2000 i)

Product details

• Authors: S. Brendle, Klaus-Joche Engel, Klaus-Jochen Engel, T. Hahn, R. Nagel, Rainer Nagel, A. Rhandi, S. Romanelli
• Publisher: Springer, Berlin
• Languages: English
• Product format: Hardback
• Released: 21.06.2001
• EAN: 9780387984636
• ISBN: 978-0-387-98463-6
• No. of pages: 589
• Dimensions: 164 mm x 40 mm x 245 mm
• Weight: 1010 g
• Illustrations: XXI, 589 p.
• Series: Graduate Texts in Mathematics; Graduate Texts in Mathematics
• Subject: Natural sciences, medicine, IT, technology > Mathematics > Arithmetic, algebra