One-Parameter Semigroups for Linear Evolution Equations (Graduate Texts in Mathematics) [Hardcover]

Klaus-Jochen Engel (Author), Rainer Nagel (Author), S. Brendle (Contributor), M. Campiti (Contributor), T. Hahn (Contributor), G. Metafune (Contributor), G. Nickel (Contributor), D. Pallara (Contributor), C. Perazzoli (Contributor), A. Rhandi (Contributor), S. Romanelli (Contributor), R. Schnaubelt (Contributor)

Book Description

Publication Date: October 29, 1999 | ISBN-10: 0387984631 | ISBN-13: 978-0387984636 | Edition: 1

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. Also, the book places an emphasis on philosophical motivation and the historical background.

Editorial Reviews

Review

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 at the 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

• Hardcover: 607 pages
• Publisher: Springer; 1 edition (October 29, 1999)
• Language: English
• ISBN-10: 0387984631
• ISBN-13: 978-0387984636
• Product Dimensions: 9.6 x 6.4 x 1.3 inches
• Shipping Weight: 2.2 pounds (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (2 customer reviews)
• Amazon Best Sellers Rank: #1,204,428 in Books (See Top 100 in Books)

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3 of 3 people found the following review helpful:

5.0 out of 5 stars Engel et al.'s One Parameter Semigroups Book, March 29, 2000

By 

Osher Doctorow, Ph.D. - See all my reviews

This review is from: One-Parameter Semigroups for Linear Evolution Equations (Graduate Texts in Mathematics) (Hardcover)

Semigroups and Clifford algebras have become two of the main trends in mathematics and mathematical physics in the last 5 years. A researcher in either area cannot afford to be without major books and journal articles in these areas, and Engel et al.'s is the best that I have seen of recent semigroup books. Their book is a Graduate Text, but it actually presents many open questions and research ideas, as is usual for Springer and Springer-Verlag publications (and also Kluwer-Plenum and Cambridge University Press). Semigroups were familiar to those of us in probability for many years because of their Markov chain/process relationships, but the astonishing fact is that Engel et al. show that non-Markov applications and non-Hilbert space (in fact, general Banach space) applications and theorems abound. For those of us who are not too fond of Markov processes (like me), and who are also not too fond of Hilbert spaces (the usual space of Quantum Mechanics which went sour and had to be repaired by A. Bohm and still seems in bad need of repair), this is really good news. Another fascinating trend is in the direction of Positive Semigroups, which ties in with ordering results and inequalities (see my review of Clarke et al.). Positive semigroups have applications to transport and delay (differential) equations and semigroups have applications to control theory which means what it sounds like: physics-engineering control of satellites, rockets, robots, and God knows what else. I repeat my usual caution: if your background is mathematically deficient in these areas, hire a reputable consultant or tutor to translate the book into plain English more or less. If the person cannot translate in one session, look for another person, or quiz them on the phone first.

2 of 2 people found the following review helpful:

5.0 out of 5 stars Outstanding Title, September 1, 2002

By 

Carlos E. M. Motta (Rio de Janeiro, RJ Brazil) - See all my reviews
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This review is from: One-Parameter Semigroups for Linear Evolution Equations (Graduate Texts in Mathematics) (Hardcover)

I guess that, besides the classic references from Pazy and Jerome Goldstein, this title outstands in its category. I've heard several words of criticism over Pazy's work due to the lack of applications and several laments over the fact that Goldstein's book is out of print. This book introduces the semigroup theory like no other: it doesn't forget the historic and philosophical aspect of subject and it's full filled with applications and deep beauty. Congrats to the authors and also to the customers that decide to buy this title, may it be PDE or Dinamic Systems, you'll be home free...