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This volume contains survey articles based on lecture series given by the authors at the Australian National University between July 2001 and June 2002. All but one were given in the seminar series of the Special Program on Spectral and Scattering Theory which was held at ANU from July to December, 2001.

Operator theory. --- Operator theory

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This volume contains survey articles based on lecture series given by the authors at the Australian National University between July 2001 and June 2002. All but one were given in the seminar series of the Special Program on Spectral and Scattering Theory which was held at ANU from July to December, 2001.

Operator theory. --- Operator theory

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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.

Operator theory

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Operator theory.

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This volume contains papers and problems presented to the Conference on Automatic Continuity and Banach Algebras, held at the Australian National University, January 2 - 20, 1989. The timing and duration of this conference was designed to fit into the January break of many northern hemisphere universities, yet to have a workshop environment to enhance interaction between participants. The articles are essentially expanded versions of the talks given at the conference, with the exception of several papers which are appearing elsewhere.

Operator theory