Download or read book Integration A Functional Approach written by Klaus Bichteler and published by Birkhäuser. This book was released on 2010-12-02 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers Lebesgue integration and its generalizations from Daniell's point of view, modified by the use of seminorms. Integrating functions rather than measuring sets is posited as the main purpose of measure theory. From this point of view Lebesgue's integral can be had as a rather straightforward, even simplistic, extension of Riemann's integral; and its aims, definitions, and procedures can be motivated at an elementary level. The notion of measurability, for example, is suggested by Littlewood's observations rather than being conveyed authoritatively through definitions of (sigma)-algebras and good-cut-conditions, the latter of which are hard to justify and thus appear mysterious, even nettlesome, to the beginner. The approach taken provides the additional benefit of cutting the labor in half. The use of seminorms, ubiquitous in modern analysis, speeds things up even further. The book is intended for the reader who has some experience with proofs, a beginning graduate student for example. It might even be useful to the advanced mathematician who is confronted with situations - such as stochastic integration - where the set-measuring approach to integration does not work.
Download or read book A Modern Approach to Functional Integration written by John R. Klauder and published by Springer Science & Business Media. This book was released on 2010-11-08 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text takes advantage of recent developments in the theory of path integration and attempts to make a major paradigm shift in how the art of functional integration is practiced. The techniques developed in the work will prove valuable to graduate students and researchers in physics, chemistry, mathematical physics, and applied mathematics who find it necessary to deal with solutions to wave equations, both quantum and beyond. A Modern Approach to Functional Integration offers insight into a number of contemporary research topics, which may lead to improved methods and results that cannot be found elsewhere in the textbook literature. Exercises are included in most chapters, making the book suitable for a one-semester graduate course on functional integration.
Download or read book Integration A Functional Approach written by Klaus Bichteler and published by Springer Science & Business Media. This book was released on 2010-11-23 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers Lebesgue integration and its generalizations from Daniell's point of view, modified by the use of seminorms. Integrating functions rather than measuring sets is posited as the main purpose of measure theory. From this point of view Lebesgue's integral can be had as a rather straightforward, even simplistic, extension of Riemann's integral; and its aims, definitions, and procedures can be motivated at an elementary level. The notion of measurability, for example, is suggested by Littlewood's observations rather than being conveyed authoritatively through definitions of (sigma)-algebras and good-cut-conditions, the latter of which are hard to justify and thus appear mysterious, even nettlesome, to the beginner. The approach taken provides the additional benefit of cutting the labor in half. The use of seminorms, ubiquitous in modern analysis, speeds things up even further. The book is intended for the reader who has some experience with proofs, a beginning graduate student for example. It might even be useful to the advanced mathematician who is confronted with situations - such as stochastic integration - where the set-measuring approach to integration does not work.
Download or read book A Functional Approach to L integration and Measure Theory written by Robert Allen Shive and published by . This book was released on 1966 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Functional Integration written by Cécile Dewitt-Morette and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: The program of the Institute covered several aspects of functional integration -from a robust mathematical foundation to many applications, heuristic and rigorous, in mathematics, physics, and chemistry. It included analytic and numerical computational techniques. One of the goals was to encourage cross-fertilization between these various aspects and disciplines. The first week was focused on quantum and classical systems with a finite number of degrees of freedom; the second week on field theories. During the first week the basic course, given by P. Cartier, was a presentation of a recent rigorous approach to functional integration which does not resort to discretization, nor to analytic continuation. It provides a definition of functional integrals simpler and more powerful than the original ones. Could this approach accommodate the works presented by the other lecturers? Although much remains to be done before answering "Yes," there seems to be no major obstacle along the road. The other courses taught during the first week presented: a) a solid introduction to functional numerical techniques (A. Sokal) and their applications to functional integrals encountered in chemistry (N. Makri). b) integrals based on Poisson processes and their applications to wave propagation (S. K. Foong), in particular a wave-restorer or wave-designer algorithm yielding the initial wave profile when one can only observe its distortion through a dissipative medium. c) the formulation of a quantum equivalence principle (H. Kleinert) which. given the flat space theory, yields a well-defined quantum theory in spaces with curvature and torsion.
Download or read book Functional Integration written by Pierre Cartier and published by Cambridge University Press. This book was released on 2006-11-30 with total page 7 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this text, Cartier and DeWitt-Morette, using their complementary interests and expertise, successfully condense and apply the essentials of Functional Integration to a great variety of systems, showing this mathematically elusive technique to be a robust, user friendly and multipurpose tool.
Download or read book The Functional Approach to Integration written by Zahra Moazami and published by . This book was released on 1979 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Functional Integration and Quantum Physics written by Barry Simon and published by American Mathematical Soc.. This book was released on 2005 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focuses on probabilistic foundations of the Feynman-Kac formula. Starting with main examples of Gaussian processes (the Brownian motion, the oscillatory process, and the Brownian bridge), this book presents four different proofs of the Feynman-Kac formula.
Download or read book Measure Integration Real Analysis written by Sheldon Axler and published by Springer Nature. This book was released on 2019-11-29 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access textbook welcomes students into the fundamental theory of measure, integration, and real analysis. Focusing on an accessible approach, Axler lays the foundations for further study by promoting a deep understanding of key results. Content is carefully curated to suit a single course, or two-semester sequence of courses, creating a versatile entry point for graduate studies in all areas of pure and applied mathematics. Motivated by a brief review of Riemann integration and its deficiencies, the text begins by immersing students in the concepts of measure and integration. Lebesgue measure and abstract measures are developed together, with each providing key insight into the main ideas of the other approach. Lebesgue integration links into results such as the Lebesgue Differentiation Theorem. The development of products of abstract measures leads to Lebesgue measure on Rn. Chapters on Banach spaces, Lp spaces, and Hilbert spaces showcase major results such as the Hahn–Banach Theorem, Hölder’s Inequality, and the Riesz Representation Theorem. An in-depth study of linear maps on Hilbert spaces culminates in the Spectral Theorem and Singular Value Decomposition for compact operators, with an optional interlude in real and complex measures. Building on the Hilbert space material, a chapter on Fourier analysis provides an invaluable introduction to Fourier series and the Fourier transform. The final chapter offers a taste of probability. Extensively class tested at multiple universities and written by an award-winning mathematical expositor, Measure, Integration & Real Analysis is an ideal resource for students at the start of their journey into graduate mathematics. A prerequisite of elementary undergraduate real analysis is assumed; students and instructors looking to reinforce these ideas will appreciate the electronic Supplement for Measure, Integration & Real Analysis that is freely available online. For errata and updates, visit https://measure.axler.net/
Download or read book Functional Integration written by Jean-Pierre Antoine and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: The idea of the workshop on Functional Integration, Theory and Applications, held in Louvain-Ia-Neuve from November 6 to 9 1979, was to put in close and informal contact, during a few days, active workers in the field. There is no doubt now that functional integration is a tool that is being applied in all branches of modern physics. Since the earlier works of Dirac and Feynman enormous progress has been made, but unfortunately we lack still a unifying and rigo rous mathematical framework to account for all the situations in which one is interested. We are then in presence of a rapid ly changing field in which new achievements, proposals, and points of view are the normal pattern. Considering this state of affairs we have decided to order the articles starting from the more fundamental and ambitious from the point of view of mathematical rigour, followed by ar ticles in which the main interest is the application to con crete physical situations. It is obvious that this ordering should not be taken too seriously since in many cases there will be an interplay of both objects.
Download or read book A Radical Approach to Lebesgue s Theory of Integration written by David M. Bressoud and published by Cambridge University Press. This book was released on 2008-01-21 with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt: Meant for advanced undergraduate and graduate students in mathematics, this introduction to measure theory and Lebesgue integration is motivated by the historical questions that led to its development. The author tells the story of the mathematicians who wrestled with the difficulties inherent in the Riemann integral, leading to the work of Jordan, Borel, and Lebesgue.
Download or read book Britain s Functional Approach to Integration written by Keith Allen Knutson and published by . This book was released on 2000 with total page 648 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Functional Approach to Data Management written by Peter M.D. Gray and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is over 20 years since the functional data model and functional programming languages were first introduced to the computing community. Although developed by separate research communities, recent work, presented in this book, suggests there is powerful synergy in their integration. As database technology emerges as central to yet more complex and demanding applications in areas such as bioinformatics, national security, criminal investigations and advanced engineering, more sophisticated approaches like those presented here, are needed. A tutorial introduction by the editors prepares the reader for the chapters that follow, written by leading researchers, including some of the early pioneers. They provide a comprehensive treatment showing how the functional approach provides for modeling, analyzis and optimization in databases, and also data integration and interoperation in heterogeneous environments. Several chapters deal with mathematical results on the transformation of expressions, fundamental to the functional approach. The book also aims to show how the approach relates to the Internet and current work on semistructured data, XML and RDF. The book presents a comprehensive view of the functional approach to data management, bringing together important material hitherto widely scattered, some new research, and a comprehensive set of references. It will serve as a valuable resource for researchers, faculty and graduate students, as well as those in industry responsible for new systems development.
Download or read book Lean Integration written by John G. Schmidt and published by Pearson Education. This book was released on 2010-05-18 with total page 685 pages. Available in PDF, EPUB and Kindle. Book excerpt: Use Lean Techniques to Integrate Enterprise Systems Faster, with Far Less Cost and Risk By some estimates, 40 percent of IT budgets are devoted to integration. However, most organizations still attack integration on a project-by-project basis, causing unnecessary expense, waste, risk, and delay. They struggle with integration “hairballs”: complex point-to-point information exchanges that are expensive to maintain, difficult to change, and unpredictable in operation. The solution is Lean Integration. This book demonstrates how to use proven “lean” techniques to take control over the entire integration process. John Schmidt and David Lyle show how to establish “integration factories” that leverage the powerful benefits of repeatability and continuous improvement across every integration project you undertake. Drawing on their immense experience, Schmidt and Lyle bring together best practices; solid management principles; and specific, measurable actions for streamlining integration development and maintenance. Whether you’re an IT manager, project leader, architect, analyst, or developer, this book will help you systematically improve the way you integrate—adding value that is both substantial and sustainable. Coverage includes Treating integration as a business strategy and implementing management disciplines that systematically address its people, process, policy, and technology dimensions Providing maximum business flexibility and supporting rapid change without compromising stability, quality, control, or efficiency Applying improvements incrementally without “Boiling the Ocean” Automating processes so you can deliver IT solutions faster–while avoiding the pitfalls of automation Building in both data and integration quality up front, rather than inspecting quality in later More than a dozen in-depth case studies that show how real organizations are applying Lean Integration practices and the lessons they’ve learned Visit integrationfactory.com for additional resources, including more case studies, best practices, templates, software demos, and reference links, plus a direct connection to lean integration practitioners worldwide.
Download or read book A Concise Introduction to the Theory of Integration written by Daniel W. Stroock and published by Springer Science & Business Media. This book was released on 1998-12-23 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: Designed for the analyst, physicist, engineer, or economist, provides such readers with most of the measure theory they will ever need. Emphasis is on the concrete aspects of the subject. Subjects include classical theory, Lebesgue's measure, Lebesgue integration, products of measures, changes of variable, some basic inequalities, and abstract theory. Annotation copyright by Book News, Inc., Portland, OR
Download or read book Measure and Integration written by Hari Bercovici and published by Springer. This book was released on 2016-03-17 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers the material of a one year course in real analysis. It includes an original axiomatic approach to Lebesgue integration which the authors have found to be effective in the classroom. Each chapter contains numerous examples and an extensive problem set which expands considerably the breadth of the material covered in the text. Hints are included for some of the more difficult problems.
Download or read book Engineering Systems Integration written by Gary O. Langford and published by CRC Press. This book was released on 2016-04-19 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first book to address the underlying premises of systems integration and how to exposit them into a practical and productive manner, this book prepares systems managers and systems engineers to consider their decisions in light of systems integration metrics. The book addresses two questions: Is there a way to express the interplay of human actions and the result of system interactions of a product with its environment, and are there methods that combine to improve the integration of systems? The systems integration theory and integration frameworks proposed in the book tie General Systems Theory with practice.
