| Summary: | 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<U+0013>Yosida and Lumer<U+0013>Phillips characterizations of semigroup generators * The Trotter<U+0013>Kato approximation theorem * Kato<U+0019>s unified treatment of the exponential formula and the Trotter product formula * The Hille<U+0013>Phillips perturbation theorem, and Stone<U+0019>s representation of unitary semigroups * Generalizations of spectral theory<U+0019>s connection to operator semigroups * A natural generalization of Stone<U+0019>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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