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A Short Course on Operator Semigroups

  • Textbook
  • © 2006

Overview

Authors:
  1. Klaus-Jochen Engel

    1. Faculty of Engineering, Division of Mathematics, Monteluco di Roio (AQ), Italy

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  2. Rainer Nagel

    1. Mathematics Institute, Tübingen University, Tübingen, Germany

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    You can also search for this author in PubMed   Google Scholar

  • 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 book series: Universitext (UTX)

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-x
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  2. Introduction

    Pages 1-33

  3. Semigroups, Generators, and Resolvents

    Pages 34-114

  4. Perturbation of Semigroups

    Pages 115-135

  5. Approximation of Semigroups

    Pages 136-155

  6. Spectral Theory and Asymptotics for Semigroups

    Pages 156-204

  7. Positive Semigroups

    Pages 205-221

  8. Back Matter

    Pages 222-248
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Keywords

About this book

ThetheoryofstronglycontinuoussemigroupsoflinearoperatorsonBanach spaces, operator semigroups for short, has become an indispensable tool in a great number of areas of modern mathematical analysis. In our Springer Graduate Text [EN00] we presented this beautiful theory, together with many applications, and tried to show the progress made since the pub- cation in 1957 of the now classical monograph [HP57] by E. Hille and R. Phillips. However, the wealth of results exhibited in our Graduate Text seems to have discouraged some of the potentially interested readers. With the present text we o?er a streamlined version that strictly sticks to the essentials. We have skipped certain parts, avoided the use of sophisticated arguments,and,occasionally,weakenedtheformulationofresultsandm- i?ed the proofs. However, to a large extent this book consists of excerpts taken from our Graduate Text, with some new material on positive se- groups added in Chapter VI. We hope that the present text will help students take their ?rst step into this interesting and lively research ?eld. On the other side, it should provide useful tools for the working mathematician. Acknowledgments This book is dedicated to our students. Without them we would not be able to do and to enjoy mathematics. Many of them read previous versions when it served as the text of our Seventh Internet Seminar 2003/04. Here Genni Fragnelli, Marc Preunkert and Mark C. Veraar were among the most active readers. Particular thanks go to Tanja Eisner, Vera Keicher, Agnes Radl for proposing considerable improvements in the ?nal version.

Reviews

"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)

 

Authors and Affiliations

  • Faculty of Engineering, Division of Mathematics, Monteluco di Roio (AQ), Italy

    Klaus-Jochen Engel

  • Mathematics Institute, Tübingen University, Tübingen, Germany

    Rainer Nagel

Bibliographic Information

  • Book Title: A Short Course on Operator Semigroups

  • Authors: Klaus-Jochen Engel, Rainer Nagel

  • Series Title: Universitext

  • DOI: https://doi.org/10.1007/0-387-36619-9

  • Publisher: Springer New York, NY

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer-Verlag New York 2006

  • Hardcover ISBN: 978-0-387-31341-2Published: 06 June 2006

  • Softcover ISBN: 978-1-4419-2174-1Published: 23 November 2010

  • eBook ISBN: 978-0-387-36619-7Published: 14 October 2006

  • Series ISSN: 0172-5939

  • Series E-ISSN: 2191-6675

  • Edition Number: 1

  • Number of Pages: X, 248

  • Topics: Operator Theory, Analysis

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