Download or read book Poincar Duality Algebras Macaulay s Dual Systems and Steenrod Operations written by Dagmar M. Meyer and published by Cambridge University Press. This book was released on 2005-08-18 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: A monograph demonstrating remarkable and unexpected interdisciplinary connections in the areas of commutative algebra, invariant theory and algebraic topology.
Download or read book Quantum Stochastic Processes and Noncommutative Geometry written by Kalyan B. Sinha and published by Cambridge University Press. This book was released on 2007-01-25 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: The classical theory of stochastic processes has important applications arising from the need to describe irreversible evolutions in classical mechanics; analogously quantum stochastic processes can be used to model the dynamics of irreversible quantum systems. Noncommutative, i.e. quantum, geometry provides a framework in which quantum stochastic structures can be explored. This book is the first to describe how these two mathematical constructions are related. In particular, key ideas of semigroups and complete positivity are combined to yield quantum dynamical semigroups (QDS). Sinha and Goswami also develop a general theory of Evans-Hudson dilation for both bounded and unbounded coefficients. The unique features of the book, including the interaction of QDS and quantum stochastic calculus with noncommutative geometry and a thorough discussion of this calculus with unbounded coefficients, will make it of interest to graduate students and researchers in functional analysis, probability and mathematical physics.
Download or read book Convexity written by Barry Simon and published by Cambridge University Press. This book was released on 2011-05-19 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: Convexity is important in theoretical aspects of mathematics and also for economists and physicists. In this monograph the author provides a comprehensive insight into convex sets and functions including the infinite-dimensional case and emphasizing the analytic point of view. Chapter one introduces the reader to the basic definitions and ideas that play central roles throughout the book. The rest of the book is divided into four parts: convexity and topology on infinite-dimensional spaces; Loewner's theorem; extreme points of convex sets and related issues, including the Krein–Milman theorem and Choquet theory; and a discussion of convexity and inequalities. The connections between disparate topics are clearly explained, giving the reader a thorough understanding of how convexity is useful as an analytic tool. A final chapter overviews the subject's history and explores further some of the themes mentioned earlier. This is an excellent resource for anyone interested in this central topic.
Download or read book Modern Approaches to the Invariant Subspace Problem written by Isabelle Chalendar and published by Cambridge University Press. This book was released on 2011-08-18 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the major unsolved problems in operator theory is the fifty-year-old invariant subspace problem, which asks whether every bounded linear operator on a Hilbert space has a nontrivial closed invariant subspace. This book presents some of the major results in the area, including many that were derived within the past few years and cannot be found in other books. Beginning with a preliminary chapter containing the necessary pure mathematical background, the authors present a variety of powerful techniques, including the use of the operator-valued Poisson kernel, various forms of the functional calculus, Hardy spaces, fixed point theorems, minimal vectors, universal operators and moment sequences. The subject is presented at a level accessible to postgraduate students, as well as established researchers. It will be of particular interest to those who study linear operators and also to those who work in other areas of pure mathematics.
Download or read book Malliavin Calculus for L vy Processes and Infinite Dimensional Brownian Motion written by Horst Osswald and published by Cambridge University Press. This book was released on 2012-03 with total page 429 pages. Available in PDF, EPUB and Kindle. Book excerpt: After functional, measure and stochastic analysis prerequisites, the author covers chaos decomposition, Skorohod integral processes, Malliavin derivative and Girsanov transformations.
Download or read book Nonlinear Perron Frobenius Theory written by Bas Lemmens and published by Cambridge University Press. This book was released on 2012-05-03 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: Guides the reader through the nonlinear Perron-Frobenius theory, introducing them to recent developments and challenging open problems.
Download or read book Normal Approximations with Malliavin Calculus written by Ivan Nourdin and published by Cambridge University Press. This book was released on 2012-05-10 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book shows how quantitative central limit theorems can be deduced by combining two powerful probabilistic techniques: Stein's method and Malliavin calculus.
Download or read book Rigidity in Higher Rank Abelian Group Actions Volume 1 Introduction and Cocycle Problem written by Anatole Katok and published by Cambridge University Press. This book was released on 2011-06-16 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained monograph presents rigidity theory for a large class of dynamical systems, differentiable higher rank hyperbolic and partially hyperbolic actions. This first volume describes the subject in detail and develops the principal methods presently used in various aspects of the rigidity theory. Part I serves as an exposition and preparation, including a large collection of examples that are difficult to find in the existing literature. Part II focuses on cocycle rigidity, which serves as a model for rigidity phenomena as well as a useful tool for studying them. The book is an ideal reference for applied mathematicians and scientists working in dynamical systems and a useful introduction for graduate students interested in entering the field. Its wealth of examples also makes it excellent supplementary reading for any introductory course in dynamical systems.
Download or read book Jordan Structures in Geometry and Analysis written by Cho-Ho Chu and published by Cambridge University Press. This book was released on 2011-11-17 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: Jordan theory has developed rapidly in the last three decades, but very few books describe its diverse applications. Here, the author discusses some recent advances of Jordan theory in differential geometry, complex and functional analysis, with the aid of numerous examples and concise historical notes. These include: the connection between Jordan and Lie theory via the Tits–Kantor–Koecher construction of Lie algebras; a Jordan algebraic approach to infinite dimensional symmetric manifolds including Riemannian symmetric spaces; the one-to-one correspondence between bounded symmetric domains and JB*-triples; and applications of Jordan methods in complex function theory. The basic structures and some functional analytic properties of JB*-triples are also discussed. The book is a convenient reference for experts in complex geometry or functional analysis, as well as an introduction to these areas for beginning researchers. The recent applications of Jordan theory discussed in the book should also appeal to algebraists.
Download or read book Mathematics of Two Dimensional Turbulence written by Sergei Kuksin and published by Cambridge University Press. This book was released on 2012-09-20 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is dedicated to the mathematical study of two-dimensional statistical hydrodynamics and turbulence, described by the 2D Navier–Stokes system with a random force. The authors' main goal is to justify the statistical properties of a fluid's velocity field u(t,x) that physicists assume in their work. They rigorously prove that u(t,x) converges, as time grows, to a statistical equilibrium, independent of initial data. They use this to study ergodic properties of u(t,x) – proving, in particular, that observables f(u(t,.)) satisfy the strong law of large numbers and central limit theorem. They also discuss the inviscid limit when viscosity goes to zero, normalising the force so that the energy of solutions stays constant, while their Reynolds numbers grow to infinity. They show that then the statistical equilibria converge to invariant measures of the 2D Euler equation and study these measures. The methods apply to other nonlinear PDEs perturbed by random forces.
Download or read book The Theory of Hardy s Z Function written by A. Ivić and published by Cambridge University Press. This book was released on 2013 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive account of Hardy's Z-function, one of the most important functions of analytic number theory.
Download or read book Distribution Modulo One and Diophantine Approximation written by Yann Bugeaud and published by Cambridge University Press. This book was released on 2012-07-05 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: A treatment of cutting-edge research on the distribution modulo one of sequences and related topics, much of it from the last decade. There are numerous exercises to aid student understanding of the topic, and researchers will appreciate the notes at the end of each chapter, extensive references and open problems.
Download or read book Polynomials and Vanishing Cycles written by Mihai Tibăr and published by Cambridge University Press. This book was released on 2007-05-17 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: A systematic geometro-topological approach to vanishing cycles appearing in non-proper fibrations is proposed in this tract. Lefschetz theory, complex Morse theory and singularities of hypersurfaces are presented in detail leading to the latest research on topics such as the topology of singularities of meromorphic functions and non-generic Lefschetz pencils.
Download or read book Singularities of the Minimal Model Program written by János Kollár and published by Cambridge University Press. This book was released on 2013-02-21 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a comprehensive treatment of the singularities that appear in the minimal model program and in the moduli problem for varieties. The study of these singularities and the development of Mori's program have been deeply intertwined. Early work on minimal models relied on detailed study of terminal and canonical singularities but many later results on log terminal singularities were obtained as consequences of the minimal model program. Recent work on the abundance conjecture and on moduli of varieties of general type relies on subtle properties of log canonical singularities and conversely, the sharpest theorems about these singularities use newly developed special cases of the abundance problem. This book untangles these interwoven threads, presenting a self-contained and complete theory of these singularities, including many previously unpublished results.
Download or read book Coherence in Three Dimensional Category Theory written by Nick Gurski and published by Cambridge University Press. This book was released on 2013-03-21 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dimension three is an important test-bed for hypotheses in higher category theory and occupies something of a unique position in the categorical landscape. At the heart of matters is the coherence theorem, of which this book provides a definitive treatment, as well as covering related results. Along the way the author treats such material as the Gray tensor product and gives a construction of the fundamental 3-groupoid of a space. The book serves as a comprehensive introduction, covering essential material for any student of coherence and assuming only a basic understanding of higher category theory. It is also a reference point for many key concepts in the field and therefore a vital resource for researchers wishing to apply higher categories or coherence results in fields such as algebraic topology or theoretical computer science.
Download or read book Induced Representations of Locally Compact Groups written by Eberhard Kaniuth and published by Cambridge University Press. This book was released on 2013 with total page 359 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive presentation of the theories of induced representations and Mackey analysis applied to a wide variety of groups.
Download or read book A Universal Construction for Groups Acting Freely on Real Trees written by Ian Chiswell and published by Cambridge University Press. This book was released on 2012-10-18 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of R-trees is a well-established and important area of geometric group theory and in this book the authors introduce a construction that provides a new perspective on group actions on R-trees. They construct a group RF(G), equipped with an action on an R-tree, whose elements are certain functions from a compact real interval to the group G. They also study the structure of RF(G), including a detailed description of centralizers of elements and an investigation of its subgroups and quotients. Any group acting freely on an R-tree embeds in RF(G) for some choice of G. Much remains to be done to understand RF(G), and the extensive list of open problems included in an appendix could potentially lead to new methods for investigating group actions on R-trees, particularly free actions. This book will interest all geometric group theorists and model theorists whose research involves R-trees.
