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OverviewThis book is based on lecture notes from a second-year graduate course, and is a greatly expanded version of our previous monograph [K8]. We expose some aspects of the theory of semigroups of linear operators, mostly (but not only) from the point of view of its meeting with that part of spectral theory which is concerned with the integral representation of families of operators. This approach and selection of topics di?erentiate this book from others in the general area, and re?ect the author’s own research directions. There is no attempt therefore to cover thoroughly the theory of semigroups of operators. This theory and its applications are extensively exposed in many books, from theclassicHille–Phillipsmonograph[HP]tothemostrecenttextbookofEngel and Nagel [EN2] (see [A], [BB], [Cl], [D3], [EN1], [EN2], [Fat], [G], [HP], [P], [Vr], and others), as well as in chapters in more general texts on Functional Analysis and the theory of linear operators (cf. [D5], [DS I–III], [Kat1], [RS], [Y], and many others). Full Product DetailsAuthor: Shmuel KantorovitzPublisher: Birkhauser Boston Inc Imprint: Birkhauser Boston Inc Edition: 2010 ed. Volume: 281 Dimensions: Width: 15.50cm , Height: 1.70cm , Length: 23.50cm Weight: 1.270kg ISBN: 9780817649319ISBN 10: 081764931 Pages: 266 Publication Date: 01 December 2009 Audience: College/higher education , Professional and scholarly , Postgraduate, Research & Scholarly , Professional & Vocational Format: Hardback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsGeneral 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.ReviewsFrom the reviews: This book is based on the author's lecture notes ! in which the more advanced parts concentrated on spectral representations. ! There is also a presentation of a well-known stability theorem for semigroups under countable spectral conditions. ! The increased variety of topics covered will make the book more useful ! . Other advantages are the inclusion of an index and some exercises, considerable extensions of the bibliography and the list of contents, and more attractive typesetting. (C. J. K. Batty, Mathematical Reviews, Issue 2010 k) From the reviews: This book is based on the author's lecture notes ... in which the more advanced parts concentrated on spectral representations. ... There is also a presentation of a well-known stability theorem for semigroups under countable spectral conditions. ... The increased variety of topics covered will make the book more useful ... . Other advantages are the inclusion of an index and some exercises, considerable extensions of the bibliography and the list of contents, and more attractive typesetting. --- (C. J. K. Batty, Mathematical Reviews, Issue 2010 k) The present graduate level text expands the previous lecture notes from the same author, Semigroups of operators and spectral theory ... . It begins with a succinct introduction to operator semigroups covering classical topics such as generators, the Hille-Yosida theorem, dissipative operators and the Lumer-Phillips theorem, the Trotter convergence theorem, exponential formulas, perturbation theory, Stone's theorem, and analytic semigroups. ... The text is also intended for second-year graduate students ... . it will be a valuable source for researchers working in this area. (G. Teschl, Monatshefte fur Mathematik, Vol. 162 (4), April, 2011) Author InformationTab Content 6Author Website:Countries AvailableAll regions |
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