A Short Course on Operator Semigroups

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Juni 2006



The book offers a direct and up-to-date introduction to the theory of one-parameter semigroups of linear operators on Banach spaces. It contains the fundamental results of the theory such as the Hille-Yoshida generation theorem, the bounded perturbation theorem, and the Trotter-Kato approximation theorem. It also treats the spectral theory of semigroups and its consequences for the qualitative behavior. The book is intended for students and researchers who want to become acquainted with the concept of semigroups in order to work with it in fields like partial and functional differential equations. Exercises are provided at the end of the chapters.


Semigroups, Generators, and Resolvents.
Perturbation of Semigroups.
Approximation of Semigroups.
Spectral Theory and Asymptotics for Semigroups.
Positive Semigroups.
Selected References to Recent Research.
List of Symbols and Abbreviations.


"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)

EAN: 9780387313412
ISBN: 0387313419
Untertitel: 2006. Auflage. Book. Sprache: Englisch.
Verlag: Springer
Erscheinungsdatum: Juni 2006
Seitenanzahl: 260 Seiten
Format: gebunden
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