Short Course on Operator Semigroups

• Semigroups, Generators, and Resolvents.- Perturbation of Semigroups.- Approximation of Semigroups.- Spectral Theory and Asymptotics for Semigroups.- Positive Semigroups.

"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)