Download or read book Operator Algebras Generated by Commuting Projections A Vector Measure Approach written by Werner Ricker and published by Springer. This book was released on 2006-11-14 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a systematic investigation of the theory of those commutative, unital subalgebras (of bounded linear operators acting in a Banach space) which are closed for some given topology and are generated by a uniformly bounded Boolean algebra of projections. One of the main aims is to employ the methods of vector measures and integration as a unifying theme throughout. This yields proofs of several classical results which are quite different to the classical ones. This book is directed to both those wishing to learn this topic for the first time and to current experts in the field.
Download or read book Positivity written by Karim Boulabiar and published by Springer Science & Business Media. This book was released on 2007-12-16 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents nine survey articles addressing topics surrounding positivity, with an emphasis on functional analysis. The book assembles a wide spectrum of research into positivity, providing up-to-date information on topics of current interest. The discussion provides insight into classical areas like spaces of continuous functions, f-algebras, and integral operators. The coverage extends is broad, including vector measures, operator spaces, ordered tensor products, and non-commutative Banach function spaces.
Download or read book Loeb Measures in Practice Recent Advances written by Nigel J. Cutland and published by Springer. This book was released on 2004-10-11 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: This expanded version of the 1997 European Mathematical Society Lectures given by the author in Helsinki, begins with a self-contained introduction to nonstandard analysis (NSA) and the construction of Loeb Measures, which are rich measures discovered in 1975 by Peter Loeb, using techniques from NSA. Subsequent chapters sketch a range of recent applications of Loeb measures due to the author and his collaborators, in such diverse fields as (stochastic) fluid mechanics, stochastic calculus of variations ("Malliavin" calculus) and the mathematical finance theory. The exposition is designed for a general audience, and no previous knowledge of either NSA or the various fields of applications is assumed.
Download or read book Optimal Domain and Integral Extension of Operators written by S. Okada and published by Springer Science & Business Media. This book was released on 2008-09-09 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with the analysis of linear operators from a quasi-Banach function space into a Banach space. The central theme is to extend the operator to as large a (function) space as possible, its optimal domain, and to take advantage of this in analyzing the original operator. Most of the material appears in print for the first time. The book has an interdisciplinary character and is aimed at graduates, postgraduates, and researchers in modern operator theory.
Download or read book Variational Methods for Problems from Plasticity Theory and for Generalized Newtonian Fluids written by Martin Fuchs and published by Springer Science & Business Media. This book was released on 2000-12-12 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: Variational methods are applied to prove the existence of weak solutions for boundary value problems from the deformation theory of plasticity as well as for the slow, steady state flow of generalized Newtonian fluids including the Bingham and Prandtl-Eyring model. For perfect plasticity the role of the stress tensor is emphasized by studying the dual variational problem in appropriate function spaces. The main results describe the analytic properties of weak solutions, e.g. differentiability of velocity fields and continuity of stresses. The monograph addresses researchers and graduate students interested in applications of variational and PDE methods in the mechanics of solids and fluids.
Download or read book Selected Preserver Problems on Algebraic Structures of Linear Operators and on Function Spaces written by L. Molnár and published by Springer. This book was released on 2006-11-15 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: The territory of preserver problems has grown continuously within linear analysis. This book presents a cross-section of the modern theory of preservers on infinite dimensional spaces (operator spaces and function spaces) through the author's corresponding results. Special emphasis is placed on preserver problems concerning some structures of Hilbert space operators which appear in quantum mechanics. In addition, local automorphisms and local isometries of operator algebras and function algebras are discussed in detail.
Download or read book Stable Approximate Evaluation of Unbounded Operators written by C. W. Groetsch and published by Springer Science & Business Media. This book was released on 2007 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spectral theory of bounded linear operators teams up with von Neumann’s theory of unbounded operators in this monograph to provide a general framework for the study of stable methods for the evaluation of unbounded operators. An introductory chapter provides numerous illustrations of unbounded linear operators that arise in various inverse problems of mathematical physics. Before the general theory of stabilization methods is developed, an extensive exposition of the necessary background material from the theory of operators on Hilbert space is provided. Several specific stabilization methods are studied in detail, with particular attention to the Tikhonov-Morozov method and its iterated version.
Download or read book Introduction to Symplectic Dirac Operators written by Katharina Habermann and published by Springer. This book was released on 2006-10-28 with total page 131 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is the first one that gives a systematic and self-contained introduction to the theory of symplectic Dirac operators and reflects the current state of the subject. At the same time, it is intended to establish the idea that symplectic spin geometry and symplectic Dirac operators may give valuable tools in symplectic geometry and symplectic topology, which have become important fields and very active areas of mathematical research.
Download or read book The Method of Approximate Inverse Theory and Applications written by Thomas Schuster and published by Springer. This book was released on 2007-04-26 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is concerned with the method of approximate inverse which is a regularization technique for stably solving inverse problems in various settings. It demonstrates the performance and functionality of the method on several examples from medical imaging and non-destructive testing, such as computerized tomography, Doppler tomography, SONAR, X-ray diffractometry and thermoacoustic computerized tomography.
Download or read book Transseries and Real Differential Algebra written by Joris van der Hoeven and published by Springer. This book was released on 2006-10-31 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: Transseries are formal objects constructed from an infinitely large variable x and the reals using infinite summation, exponentiation and logarithm. They are suitable for modeling "strongly monotonic" or "tame" asymptotic solutions to differential equations and find their origin in at least three different areas of mathematics: analysis, model theory and computer algebra. They play a crucial role in Écalle's proof of Dulac's conjecture, which is closely related to Hilbert's 16th problem. The aim of the present book is to give a detailed and self-contained exposition of the theory of transseries, in the hope of making it more accessible to non-specialists.
Download or read book Open Quantum Systems I written by Stéphane Attal and published by Springer. This book was released on 2006-08-18 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: Understanding dissipative dynamics of open quantum systems remains a challenge in mathematical physics. This problem is relevant in various areas of fundamental and applied physics. Significant progress in the understanding of such systems has been made recently. These books present the mathematical theories involved in the modeling of such phenomena. They describe physically relevant models, develop their mathematical analysis and derive their physical implications.
Download or read book Open Quantum Systems II written by Stéphane Attal and published by Springer Science & Business Media. This book was released on 2006-06-07 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: Understanding dissipative dynamics of open quantum systems remains a challenge in mathematical physics. This problem is relevant in various areas of fundamental and applied physics. Significant progress in the understanding of such systems has been made recently. These books present the mathematical theories involved in the modeling of such phenomena. They describe physically relevant models, develop their mathematical analysis and derive their physical implications.
Download or read book Sharp Real Part Theorems written by Gershon Kresin and published by Springer. This book was released on 2007-03-05 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a coherent point of view on various sharp pointwise inequalities for analytic functions in a disk in terms of the real part of the function on the boundary circle or in the disk itself. Inequalities of this type are frequently used in the theory of entire functions and in the analytic number theory.
Download or read book Filtration in Porous Media and Industrial Application written by M.S. Espedal and published by Springer Science & Business Media. This book was released on 2000-12-12 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the presentation of some flow problems in porous media having relevant industrial applications. The main topics covered are: the manufacturing of composite materials, the espresso coffee brewing process, the filtration of liquids through diapers, various questions about flow problems in oil reservoirs and the theory of homogenization. The aim is to show that filtration problems arising in very practical industrial context exhibit interesting and highly nontrivial mathematical aspects. Thus the style of the book is mathematically rigorous, but specifically oriented towards applications, so that it is intended for both applied mathematicians and researchers in various areas of technological interest. The reader is required to have a good knowledge of the classical theory of PDE and basic functional analysis.
Download or read book Similarity Problems and Completely Bounded Maps written by Gilles Pisier and published by Springer. This book was released on 2004-10-12 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes revolve around three similarity problems, appearing in three different contexts, but all dealing with the space B(H) of all bounded operators on a complex Hilbert space H. The first one deals with group representations, the second one with C* -algebras and the third one with the disc algebra. We describe them in detail in the introduction which follows. This volume is devoted to the background necessary to understand these three problems, to the solutions that are known in some special cases and to numerous related concepts, results, counterexamples or extensions which their investigation has generated. While the three problems seem different, it is possible to place them in a common framework using the key concept of "complete boundedness", which we present in detail. Using this notion, the three problems can all be formulated as asking whether "boundedness" implies "complete boundedness" for linear maps satisfying certain additional algebraic identities.
Download or read book Dynamical Systems Graphs and Algorithms written by George Osipenko and published by Springer. This book was released on 2006-10-28 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes a family of algorithms for studying the global structure of systems. By a finite covering of the phase space we construct a directed graph with vertices corresponding to cells of the covering and edges corresponding to admissible transitions. The method is used, among other things, to locate the periodic orbits and the chain recurrent set, to construct the attractors and their basins, to estimate the entropy, and more.
Download or read book Nonlinear Potential Theory and Weighted Sobolev Spaces written by Bengt O. Turesson and published by Springer Science & Business Media. This book was released on 2000-06-21 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book systematically develops the nonlinear potential theory connected with the weighted Sobolev spaces, where the weight usually belongs to Muckenhoupt's class of Ap weights. These spaces occur as solutions spaces for degenerate elliptic partial differential equations. The Sobolev space theory covers results concerning approximation, extension, and interpolation, Sobolev and Poincaré inequalities, Maz'ya type embedding theorems, and isoperimetric inequalities. In the chapter devoted to potential theory, several weighted capacities are investigated. Moreover, "Kellogg lemmas" are established for various concepts of thinness. Applications of potential theory to weighted Sobolev spaces include quasi continuity of Sobolev functions, Poincaré inequalities, and spectral synthesis theorems.
