TY  - BOOK
AU  - Kantorovitz,Shmuel
ED  - SpringerLink (Online service)
TI  - Topics in Operator Semigroups
T2  - Progress in Mathematics
SN  - 9780817649326
AV  - QA329-329.9 
U1  - 515.724 23
PY  - 2010///
CY  - Boston
PB  - Birkhäuser Boston
KW  - Mathematics
KW  - Algebra
KW  - Group theory
KW  - Operator theory
KW  - Operator Theory
KW  - Group Theory and Generalizations
N1  - General Theory -- Basic Theory -- The Semi-Simplicity Space for Groups -- Analyticity -- The Semigroup as a Function of its Generator -- Large Parameter -- Boundary Values -- Pre-Semigroups -- Integral Representations -- The Semi-Simplicity Space -- The Laplace–Stieltjes Space -- Families of Unbounded Symmetric Operators -- A Taste of Applications -- Analytic Families of Evolution Systems -- Similarity
N2  - 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
UR  - http://148.231.10.114:2048/login?url=http://link.springer.com/book/10.1007/978-0-8176-4932-6
ER  -