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Functional Analysis And The Feynman Operator Calculus
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Book Synopsis Functional Analysis and the Feynman Operator Calculus by : Tepper Gill
Download or read book Functional Analysis and the Feynman Operator Calculus written by Tepper Gill and published by Springer. This book was released on 2016-03-30 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides the mathematical foundations for Feynman's operator calculus and for the Feynman path integral formulation of quantum mechanics as a natural extension of analysis and functional analysis to the infinite-dimensional setting. In one application, the results are used to prove the last two remaining conjectures of Freeman Dyson for quantum electrodynamics. In another application, the results are used to unify methods and weaken domain requirements for non-autonomous evolution equations. Other applications include a general theory of Lebesgue measure on Banach spaces with a Schauder basis and a new approach to the structure theory of operators on uniformly convex Banach spaces. This book is intended for advanced graduate students and researchers.
Book Synopsis Feynman's Operational Calculus and Beyond by : Gerald W Johnson
Download or read book Feynman's Operational Calculus and Beyond written by Gerald W Johnson and published by OUP Oxford. This book was released on 2015-08-06 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is aimed at providing a coherent, essentially self-contained, rigorous and comprehensive abstract theory of Feynman's operational calculus for noncommuting operators. Although it is inspired by Feynman's original heuristic suggestions and time-ordering rules in his seminal 1951 paper An operator calculus having applications in quantum electrodynamics, as will be made abundantly clear in the introduction (Chapter 1) and elsewhere in the text, the theory developed in this book also goes well beyond them in a number of directions which were not anticipated in Feynman's work. Hence, the second part of the main title of this book. The basic properties of the operational calculus are developed and certain algebraic and analytic properties of the operational calculus are explored. Also, the operational calculus will be seen to possess some pleasant stability properties. Furthermore, an evolution equation and a generalized integral equation obeyed by the operational calculus are discussed and connections with certain analytic Feynman integrals are noted. This volume is essentially self-contained and we only assume that the reader has a reasonable, graduate level, background in analysis, measure theory and functional analysis or operator theory. Much of the necessary remaining background is supplied in the text itself.
Book Synopsis The Feynman Integral and Feynman's Operational Calculus by : Gerald W. Johnson
Download or read book The Feynman Integral and Feynman's Operational Calculus written by Gerald W. Johnson and published by Clarendon Press. This book was released on 2000-03-16 with total page 790 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides the most comprehensive mathematical treatment to date of the Feynman path integral and Feynman's operational calculus. It is accessible to mathematicians, mathematical physicists and theoretical physicists. Including new results and much material previously only available in the research literature, this book discusses both the mathematics and physics background that motivate the study of the Feynman path integral and Feynman's operational calculus, and also provides more detailed proofs of the central results.
Book Synopsis Applications of Functional Analysis and Operator Theory by : V. Hutson
Download or read book Applications of Functional Analysis and Operator Theory written by V. Hutson and published by Elsevier. This book was released on 2005-02-08 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: Functional analysis is a powerful tool when applied to mathematical problems arising from physical situations. The present book provides, by careful selection of material, a collection of concepts and techniques essential for the modern practitioner. Emphasis is placed on the solution of equations (including nonlinear and partial differential equations). The assumed background is limited to elementary real variable theory and finite-dimensional vector spaces. Provides an ideal transition between introductory math courses and advanced graduate study in applied mathematics, the physical sciences, or engineering Gives the reader a keen understanding of applied functional analysis, building progressively from simple background material to the deepest and most significant results Introduces each new topic with a clear, concise explanation Includes numerous examples linking fundamental principles with applications Solidifies the reader's understanding with numerous end-of-chapter problems
Book Synopsis Lectures and Exercises on Functional Analysis by : Александр Яковлевич Хелемский
Download or read book Lectures and Exercises on Functional Analysis written by Александр Яковлевич Хелемский and published by American Mathematical Society(RI). This book was released on 2006 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains a unique exposition intended to serve as an introduction to functional analysis. The topics covered include: normed spaces and bounded operators, Banach spaces, polynormed spaces and distributions, compact operators, $C*$ algebra, spectral theorems, Fourier transform, and more. A distinguishing feature of the book is the wide use of the language and elementary constructions of category theory, which are explained in the opening chapter of the book. Among nonstandard topics discussed in the book are the theory of Banach tensor products, basics of quantum functional analysis, and Borel operator calculus. General definitions and main results are supplemented with many examples and exercises. Prerequisites for the main part of the book include standard undergraduate courses in algebra and analysis. It is suitable for graduate students and researchers interested in functional analysis.
Book Synopsis Twelve Papers on Functional Analysis and Geometry by :
Download or read book Twelve Papers on Functional Analysis and Geometry written by and published by American Mathematical Soc.. This book was released on 1969-12-31 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Functional Analysis by : Yurij M. Berezansky
Download or read book Functional Analysis written by Yurij M. Berezansky and published by Birkhäuser. This book was released on 2012-12-06 with total page 443 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Functional Analysis" is a comprehensive, 2-volume treatment of a subject lying at the core of modern analysis and mathematical physics. The first volume reviews basic concepts such as the measure, the integral, Banach spaces, bounded operators and generalized functions. Volume II moves on to more advanced topics including unbounded operators, spectral decomposition, expansion in generalized eigenvectors, rigged spaces, and partial differential operators. This text provides students of mathematics and physics with a clear introduction into the above concepts, with the theory well illustrated by a wealth of examples. Researchers will appreciate it as a useful reference manual.
Book Synopsis Convex Functional Analysis by : Andrew J. Kurdila
Download or read book Convex Functional Analysis written by Andrew J. Kurdila and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is dedicated to the fundamentals of convex functional analysis. It presents those aspects of functional analysis that are extensively used in various applications to mechanics and control theory. The purpose of the text is essentially two-fold. On the one hand, a bare minimum of the theory required to understand the principles of functional, convex and set-valued analysis is presented. Numerous examples and diagrams provide as intuitive an explanation of the principles as possible. On the other hand, the volume is largely self-contained. Those with a background in graduate mathematics will find a concise summary of all main definitions and theorems.
Book Synopsis Functional Analysis and Semi-groups by : Einar Hille
Download or read book Functional Analysis and Semi-groups written by Einar Hille and published by American Mathematical Soc.. This book was released on 1996-02-06 with total page 808 pages. Available in PDF, EPUB and Kindle. Book excerpt: Early in 1952 it became obvious that a new printing would be needed, and new advances in the theory called for extensive revision. It has been completely rewritten, mostly by Phillips, and much has been added while keeping the existing framework. Thus, the algebraic tools play a major role, and are introduced early, leading to a more satisfactory operational calculus and spectral theory. The Laplace-Stieltjes transform methods, used by Hille, have not been replaced but rather supplemented by the new tools. - Foreword.
Book Synopsis Applied Functional Analysis by : J. Tinsley Oden
Download or read book Applied Functional Analysis written by J. Tinsley Oden and published by CRC Press. This book was released on 2017-12-01 with total page 695 pages. Available in PDF, EPUB and Kindle. Book excerpt: Applied Functional Analysis, Third Edition provides a solid mathematical foundation for the subject. It motivates students to study functional analysis by providing many contemporary applications and examples drawn from mechanics and science. This well-received textbook starts with a thorough introduction to modern mathematics before continuing with detailed coverage of linear algebra, Lebesque measure and integration theory, plus topology with metric spaces. The final two chapters provides readers with an in-depth look at the theory of Banach and Hilbert spaces before concluding with a brief introduction to Spectral Theory. The Third Edition is more accessible and promotes interest and motivation among students to prepare them for studying the mathematical aspects of numerical analysis and the mathematical theory of finite elements.
Book Synopsis Operator Theory in Function Spaces by : Kehe Zhu
Download or read book Operator Theory in Function Spaces written by Kehe Zhu and published by American Mathematical Soc.. This book was released on 2007 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers Toeplitz operators, Hankel operators, and composition operators on both the Bergman space and the Hardy space. The setting is the unit disk and the main emphasis is on size estimates of these operators: boundedness, compactness, and membership in the Schatten classes. Most results concern the relationship between operator-theoretic properties of these operators and function-theoretic properties of the inducing symbols. Thus a good portion of the book is devoted to the study of analytic function spaces such as the Bloch space, Besov spaces, and BMOA, whose elements are to be used as symbols to induce the operators we study. The book is intended for both research mathematicians and graduate students in complex analysis and operator theory. The prerequisites are minimal; a graduate course in each of real analysis, complex analysis, and functional analysis should sufficiently prepare the reader for the book. Exercises and bibliographical notes are provided at the end of each chapter. These notes will point the reader to additional results and problems. Kehe Zhu is a professor of mathematics at the State University of New York at Albany. His previous books include Theory of Bergman Spaces (Springer, 2000, with H. Hedenmalm and B. Korenblum) and Spaces of Holomorphic Functions in the Unit Ball (Springer, 2005). His current research interests are holomorphic function spaces and operators acting on them.
Book Synopsis Algebraic Methods in Functional Analysis by : Ivan G. Todorov
Download or read book Algebraic Methods in Functional Analysis written by Ivan G. Todorov and published by Springer Science & Business Media. This book was released on 2013-10-25 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume comprises the proceedings of the Conference on Operator Theory and its Applications held in Gothenburg, Sweden, April 26-29, 2011. The conference was held in honour of Professor Victor Shulman on the occasion of his 65th birthday. The papers included in the volume cover a large variety of topics, among them the theory of operator ideals, linear preservers, C*-algebras, invariant subspaces, non-commutative harmonic analysis, and quantum groups, and reflect recent developments in these areas. The book consists of both original research papers and high quality survey articles, all of which were carefully refereed.
Book Synopsis Functional Analysis and Related Fields by : F. E. Browder
Download or read book Functional Analysis and Related Fields written by F. E. Browder and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: On May 20-24. 1968, a Conference on Functional Analysis and Related Fields was held at the Center for Continuing Education of the University cl Chicago in honor of ProfessoLMARSHALL HARVEY STONE on the occasion of his retirement from active service at the University. The Conference received support from the Air Force Office of Scientific Research under the Grant AFOSR 68-1497. The Organizing committee for this Conference consisted of ALBERTO P. CALDERON, SAUNDERS MACLANE, ROBERT G. POHRER, and FELIX E. BROWDER (Chairman). The present volume contains some of the papers presented at the Conference. nther talks which were presented at the Conference for which papers are noLinduded hereare: K. CHANDRASEKHARAN, "Zeta functions of quadratic fields"; J. L. DooB, "An application of prob ability theory to the Choquet boundary" ; HALMOS, "Irreducible operators"; P. R. KADISON, "Strong continuity of operator functions"; L. NIRENBERG, "Intrinsic norms on complex manifolds"; D. SCOTT, "Some problems and recent results in Boolean algebras"; 1. M. SINGER, "A conjecture relating the Reidemeister torsion and the zeta function of the Laplacian". A banquet in honor of Professor STONE was held during the Con ference, with brief talks by S. S. CHERN, A. A. ALBERT, S. MACLANE, E. HEWITT, K. CHANDRASEKHARAN, and F. E. BROWDER (as Toast master), as weH as a response by Professor STONE.
Book Synopsis Functional Analysis, Approximation Theory, and Numerical Analysis by : John Michael Rassias
Download or read book Functional Analysis, Approximation Theory, and Numerical Analysis written by John Michael Rassias and published by World Scientific. This book was released on 1994 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of papers written by outstanding mathematicians. It deals with both theoretical and applied aspects of the mathematical contributions of BANACH, ULAM, and OSTROWSKI, which broaden the horizons of Functional Analysis, Approximation Theory, and Numerical Analysis in accordance with contemporary mathematical standards.
Book Synopsis Applied Functional Analysis. Approximation Methods and Computers by : S.S. Kutateladze
Download or read book Applied Functional Analysis. Approximation Methods and Computers written by S.S. Kutateladze and published by CRC Press. This book was released on 2010-12-12 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the most remarkable papers of L.V. Kantorovich in applied and numerical mathematics. It explores the principal directions of Kantorovich's research in approximate methods. The book covers descriptive set theory and functional analysis in semi-ordered vector spaces.
Book Synopsis Lectures and Exercises on Functional Analysis by : Александр Яковлевич Хелемский
Download or read book Lectures and Exercises on Functional Analysis written by Александр Яковлевич Хелемский and published by American Mathematical Soc.. This book was released on 2006 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is based on courses taught by the author at Moscow State University. Compared to many other books on the subject, it is unique in that the exposition is based on extensive use of the language and elementary constructions of category theory. Among topics featured in the book are the theory of Banach and Hilbert tensor products, the theory of distributions and weak topologies, and Borel operator calculus. The book contains many examples illustrating the general theory presented, as well as multiple exercises that help the reader to learn the subject. It can be used as a textbook on selected topics of functional analysis and operator theory. Prerequisites include linear algebra, elements of real analysis, and elements of the theory of metric spaces.
Book Synopsis Real and Functional Analysis by : Vladimir I. Bogachev
Download or read book Real and Functional Analysis written by Vladimir I. Bogachev and published by Springer Nature. This book was released on 2020-02-25 with total page 586 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on lectures given at "Mekhmat", the Department of Mechanics and Mathematics at Moscow State University, one of the top mathematical departments worldwide, with a rich tradition of teaching functional analysis. Featuring an advanced course on real and functional analysis, the book presents not only core material traditionally included in university courses of different levels, but also a survey of the most important results of a more subtle nature, which cannot be considered basic but which are useful for applications. Further, it includes several hundred exercises of varying difficulty with tips and references. The book is intended for graduate and PhD students studying real and functional analysis as well as mathematicians and physicists whose research is related to functional analysis.
