Functional Analysis And The Feynman Operator Calculus PDF Download
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| Author | : Tepper Gill |
| Publisher | : Springer |
| Total Pages | : 370 |
| Release | : 2016-03-30 |
| Genre | : Mathematics |
| ISBN | : 331927595X |
Download Functional Analysis and the Feynman Operator Calculus Book in PDF, ePub and Kindle
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.
| Author | : Gerald W. Johnson |
| Publisher | : Oxford Mathematical Monographs |
| Total Pages | : 385 |
| Release | : 2015 |
| Genre | : Biography & Autobiography |
| ISBN | : 0198702493 |
Download Feynman's Operational Calculus and Beyond Book in PDF, ePub and Kindle
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.
| Author | : Gerald W. Johnson |
| Publisher | : Clarendon Press |
| Total Pages | : 790 |
| Release | : 2000-03-16 |
| Genre | : Mathematics |
| ISBN | : 0191546267 |
Download The Feynman Integral and Feynman's Operational Calculus Book in PDF, ePub and Kindle
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.
| Author | : V. Hutson |
| Publisher | : Elsevier |
| Total Pages | : 442 |
| Release | : 2005-02-08 |
| Genre | : Mathematics |
| ISBN | : 0080527310 |
Download Applications of Functional Analysis and Operator Theory Book in PDF, ePub and Kindle
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
| Author | : Michael Pedersen |
| Publisher | : Routledge |
| Total Pages | : 312 |
| Release | : 2018-10-03 |
| Genre | : Mathematics |
| ISBN | : 1351446908 |
Download Functional Analysis in Applied Mathematics and Engineering Book in PDF, ePub and Kindle
Presenting excellent material for a first course on functional analysis , Functional Analysis in Applied Mathematics and Engineering concentrates on material that will be useful to control engineers from the disciplines of electrical, mechanical, and aerospace engineering. This text/reference discusses: rudimentary topology Banach's fixed point theorem with applications L^p-spaces density theorems for testfunctions infinite dimensional spaces bounded linear operators Fourier series open mapping and closed graph theorems compact and differential operators Hilbert-Schmidt operators Volterra equations Sobolev spaces control theory and variational analysis Hilbert Uniqueness Method boundary element methods Functional Analysis in Applied Mathematics and Engineering begins with an introduction to the important, abstract basic function spaces and operators with mathematical rigor, then studies problems in the Hilbert space setting. The author proves the spectral theorem for unbounded operators with compact inverses and goes on to present the abstract evolution semigroup theory for time dependent linear partial differential operators. This structure establishes a firm foundation for the more advanced topics discussed later in the text.
| Author | : Александр Яковлевич Хелемский |
| Publisher | : American Mathematical Society(RI) |
| Total Pages | : 468 |
| Release | : 2006 |
| Genre | : Functional analysis |
| ISBN | : 9780821835524 |
Download Lectures and Exercises on Functional Analysis Book in PDF, ePub and Kindle
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.
| Author | : Semën Samsonovich Kutateladze |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 289 |
| Release | : 2013-03-09 |
| Genre | : Mathematics |
| ISBN | : 9401587558 |
Download Fundamentals of Functional Analysis Book in PDF, ePub and Kindle
to the English Translation This is a concise guide to basic sections of modern functional analysis. Included are such topics as the principles of Banach and Hilbert spaces, the theory of multinormed and uniform spaces, the Riesz-Dunford holomorphic functional calculus, the Fredholm index theory, convex analysis and duality theory for locally convex spaces. With standard provisos the presentation is self-contained, exposing about a h- dred famous "named" theorems furnished with complete proofs and culminating in the Gelfand-Nalmark-Segal construction for C*-algebras. The first Russian edition was printed by the Siberian Division of "Nauka" P- lishers in 1983. Since then the monograph has served as the standard textbook on functional analysis at the University of Novosibirsk. This volume is translated from the second Russian edition printed by the Sobolev Institute of Mathematics of the Siberian Division of the Russian Academy of Sciences· in 1995. It incorporates new sections on Radon measures, the Schwartz spaces of distributions, and a supplementary list of theoretical exercises and problems. This edition was typeset using AMS-'lEX, the American Mathematical Society's 'lEX system. To clear my conscience completely, I also confess that := stands for the definor, the assignment operator, signifies the end of the proof.
| Author | : Alampallam V. Balakrishnan |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 385 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461258650 |
Download Applied Functional Analysis Book in PDF, ePub and Kindle
In preparing the second edition, I have taken advantage of the opportunity to correct errors as well as revise the presentation in many places. New material has been included, in addition, reflecting relevant recent work. The help of many colleagues (and especially Professor J. Stoer) in ferreting out errors is gratefully acknowledged. I also owe special thanks to Professor v. Sazonov for many discussions on the white noise theory in Chapter 6. February, 1981 A. V. BALAKRISHNAN v Preface to the First Edition The title "Applied Functional Analysis" is intended to be short for "Functional analysis in a Hilbert space and certain of its applications," the applications being drawn mostly from areas variously referred to as system optimization or control systems or systems analysis. One of the signs of the times is a discernible tilt toward application in mathematics and conversely a greater level of mathematical sophistication in the application areas such as economics or system science, both spurred undoubtedly by the heightening pace of digital computer usage. This book is an entry into this twilight zone. The aspects of functional analysis treated here are rapidly becoming essential in the training at the advance graduate level of system scientists and/or mathematical economists. There are of course now available many excellent treatises on functional analysis.
| Author | : Nino Boccara |
| Publisher | : Elsevier |
| Total Pages | : 342 |
| Release | : 1990-10-25 |
| Genre | : Mathematics |
| ISBN | : 0080916961 |
Download Functional Analysis Book in PDF, ePub and Kindle
Based on a third-year course for French students of physics, this book is a graduate text in functional analysis emphasizing applications to physics. It introduces Lebesgue integration, Fourier and Laplace transforms, Hilbert space theory, theory of distribution a la Laurent Schwartz, linear operators, and spectral theory. It contains numerous examples and completely worked out exercises.
| Author | : Peter D. Lax |
| Publisher | : John Wiley & Sons |
| Total Pages | : 451 |
| Release | : 2014-08-28 |
| Genre | : Mathematics |
| ISBN | : 1118626745 |
Download Functional Analysis Book in PDF, ePub and Kindle
Includes sections on the spectral resolution and spectral representation of self adjoint operators, invariant subspaces, strongly continuous one-parameter semigroups, the index of operators, the trace formula of Lidskii, the Fredholm determinant, and more. Assumes prior knowledge of Naive set theory, linear algebra, point set topology, basic complex variable, and real variables. Includes an appendix on the Riesz representation theorem.
