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Topics in Operator Semigroups
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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.
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