Topics in Operator Semigroups (Progress in Mathematics)

• Publisher:   Birkhäuser Boston
• Number Of Pages:   257
• Publication Date:   2009-11-11
• ISBN-10 / ASIN:   081764931X
• ISBN-13 / EAN:   9780817649319

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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