Kantorovitz, Shmuel. creator author. SpringerLink (Online service) text xxu 2010 monographic eng

electronic

electronic resource

access online resource. 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. 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. by Shmuel Kantorovitz. MATHEMATICS ALGEBRA GROUP THEORY OPERATOR THEORY MATHEMATICS OPERATOR THEORY GROUP THEORY AND GENERALIZATIONS ALGEBRA 515.724 9780817649326 99780817649326 http://dx.doi.org/10.1007/978-0-8176-4932-6 http://dx.doi.org/10.1007/978-0-8176-4932-6 100301 20260521092032.0 978-0-8176-4932-6