Semigroups of operators and spectral theory
著者
書誌事項
Semigroups of operators and spectral theory
（Pitman research notes in mathematics series, 330）
Longman , Wiley, 1995
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注記
Includes bibliographical references (p. 132-135)
内容説明・目次
内容説明
This book presents some aspects of the theory of semigroups of operators, mostly from the point of view of its interaction withspectral theory. In order to make it self-contained, a concise description of the basic theory of semigroups, with complete proofs, is included in Part I. Some of the author's recent results, such as the construction of the Hille-Yosida space for general operators, the semi-simplicity manifold, and a Taylor formula for semigroups as functions of their generator, are also included in Part I.
Part II describes recent generalizations (most of them in bookform for the first time), including pre-semigroups, semi-simplicity manifolds in situations more general than that considered in Part I, semigroups of unbounded symmetric operators, and an analogous result on "local cosine families" and semi-analytic vectors. It is hoped that this book will inspire more research in this field. This book will be of particular interest to graduate students and researchers working operator theory and its applications.
目次
Introduction
The Hille-Yosida theory
The Hille-Yosida space
Dissipativity
The Trotter-Kato convergence theorem
Exponential formulas
The Hille-Phillips perturbation theorem
Groups and semi-simplicity manifold
Analyticity
Non-commutative Taylor formula
Pre-semigroups
Semi-simplicity manifold (real spectrum case)
Semi-simplicity manifold (case R = C p(-A0))
Laplace-Stieltjes space
Semigroups of unbounded symmetrick operators
Local cosine families of symmetrick operators
Notes and references
Bibliography
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