The theory of operator semigroups was essentially discovered in the early 1930s. Since then, the theory has developed into a rich and exciting area of functional analysis and has been applied to various mathematical topics such as Markov processes, the abstract Cauchy problem, evolution equations, and mathematical physics.
This self-contained monograph focuses primarily on the theoretical connection between the theory of operator semigroups and spectral theory. Divided into three parts with a total of twelve distinct chapters, this book gives an in-depth account of the subject with numerous examples, detailed proofs, and a brief look at a few applications.
Topics include:
* The Hille-Yosida and Lumer-Phillips characterizations of semigroup generators
* The Trotter-Kato approximation theorem
* Kato´s unified treatment of the exponential formula and the Trotter product formula
* The Hille-Phillips perturbation theorem, and Stone´s representation of unitary semigroups
* Generalizations of spectral theory´s connection to operator semigroups
* A natural generalization of Stone´s spectral integral representation to a Banach space setting
With a collection of miscellaneous exercises at the end of the book and an introductory chapter examining the basic theory involved, this monograph is suitable for second-year graduate students interested in operator semigroups.
