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＜電子ブック＞
Topics in Operator Semigroups / by Shmuel Kantorovitz
(Progress in Mathematics. ISSN:2296505X ; 281)

版	1st ed. 2010.
出版者	(Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser)
出版年	2010
本文言語	英語
大きさ	XIV, 266 p : online resource
著者標目	*Kantorovitz, Shmuel author SpringerLink (Online service)
件　名	LCSH:Operator theory LCSH:Group theory LCSH:Algebra FREE:Operator Theory FREE:Group Theory and Generalizations FREE:Algebra
一般注記	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#x2013;Stieltjes Space -- Families of Unbounded Symmetric Operators -- A Taste of Applications -- Analytic Families of Evolution Systems -- Similarity 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 HTTP:URL=https://doi.org/10.1007/978-0-8176-4932-6

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