A Short Course on Operator Semigroups by Klaus-Jochen Engel

A Short Course on Operator Semigroups by Klaus-Jochen Engel

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.

"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 equationsHowever, 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)

 

Gisü¾Ž†”¼le Ruiz Goldstein is Professor, Department of Mathematical Sciences, University of Memphis, Tennessee. She is the author of more than 40 journal articles and coeditor of four books. Her research interests include partial differential equations, semigroups of operators, and mathematical physics. She received the B.S. (1980) and Ph.D. (1986) degrees in mathematics from Tulane University, New Orleans, Louisiana. Rainer Nagel is Professor of Mathematics, University of Tü¾˜¶˜¼bingen, Germany. He is the author of nearly 100 research papers and two books and is editor-in-chief of the Journal of Evolution Equations. He also serves on the editorial boards of Semigroup Forum, Positivity, and several other journals. Professor Nagel is a member of Deutsche Maathematiker Vereinigung, the Unione Matematica Italiana, the American Mathematical Society, and the Society for Industrial and Applied Mathematics and serves as coordinator of the TULKA research group. Professor Nagel received the Ph.D. degree (1969) and Habilitation (1973) from the University of Tü¾˜¶˜¼bingen, Germany. Silvia Romanelli is Associate Professor, Department of Mathematics, University of Bari, Italy. The author or coauthor of nearly 50 papers, her research interests include problems of existence and regularity of semigroups generated by differential operators and their applications. The coordinator of research and mobility programs, she is a member of the Unione Matematica Italiana and the European Mathematical Society. She received the degree (1973) in mathematics from the University of Bari, Italy.

SKU	Unavailable
ISBN 13	9780387313412
ISBN 10	0387313419
Title	A Short Course on Operator Semigroups
Author	Klaus-Jochen Engel
Series	Universitext
Condition	Unavailable
Binding Type	Hardback
Publisher	Springer-Verlag New York Inc.
Year published	2006-06-06
Number of pages	248
Cover note	Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
Note	Unavailable