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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.
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.
Concerned with the interplay between the theory of operator semigroups and spectral theory
The basics on operator semigroups are concisely covered in this self-contained text
Part I deals with 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
Part II explores generalizations of spectral theory's connection to operator semigroups
Suitable for a graduate seminar on operator semigroups or for self study
Includes supplementary material: [...]
| Erscheinungsjahr: | 2009 |
|---|---|
| Fachbereich: | Analysis |
| Genre: | Importe, Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Buch |
| Inhalt: |
xiv
266 S. |
| ISBN-13: | 9780817649319 |
| ISBN-10: | 081764931X |
| Sprache: | Englisch |
| Herstellernummer: | 12616275 |
| Einband: | Gebunden |
| Autor: | Kantorovitz, Shmuel |
| Auflage: | 2010 edition |
| Hersteller: |
Birkhauser Boston
Birkhäuser Boston |
| Verantwortliche Person für die EU: | Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, D-14197 Berlin, juergen.hartmann@springer.com |
| Maße: | 240 x 164 x 28 mm |
| Von/Mit: | Shmuel Kantorovitz |
| Erscheinungsdatum: | 01.12.2009 |
| Gewicht: | 0,548 kg |
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