Release Date: 10 December 1010
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.
* The Hillea "Yosida and Lumera "Phillips characterizations of semigroup generators
* The Trottera "Kato approximation theorem
* Katoa (TM)s unified treatment of the exponential formula and the Trotter product formula
* The Hillea "Phillips perturbation theorem, and Stonea (TM)s representation of unitary semigroups
* Generalizations of spectral theorya (TM)s connection to operator semigroups
* A natural generalization of Stonea (TM)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.
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