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)
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