Functional Analysis
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Linear Functional Analysis
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Author :
language : en
Publisher: 清华大学出版社有限公司
Release Date : 2005
Linear Functional Analysis written by and has been published by 清华大学出版社有限公司 this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Functional analysis categories.
Theorems And Problems In Functional Analysis
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Author : A. A. Kirillov
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Theorems And Problems In Functional Analysis written by A. A. Kirillov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Even the simplest mathematical abstraction of the phenomena of reality the real line-can be regarded from different points of view by different mathematical disciplines. For example, the algebraic approach to the study of the real line involves describing its properties as a set to whose elements we can apply" operations," and obtaining an algebraic model of it on the basis of these properties, without regard for the topological properties. On the other hand, we can focus on the topology of the real line and construct a formal model of it by singling out its" continuity" as a basis for the model. Analysis regards the line, and the functions on it, in the unity of the whole system of their algebraic and topological properties, with the fundamental deductions about them obtained by using the interplay between the algebraic and topological structures. The same picture is observed at higher stages of abstraction. Algebra studies linear spaces, groups, rings, modules, and so on. Topology studies structures of a different kind on arbitrary sets, structures that give mathe matical meaning to the concepts of a limit, continuity, a neighborhood, and so on. Functional analysis takes up topological linear spaces, topological groups, normed rings, modules of representations of topological groups in topological linear spaces, and so on. Thus, the basic object of study in functional analysis consists of objects equipped with compatible algebraic and topological structures.
Functional Analysis
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Author : Yuli Eidelman
language : en
Publisher: American Mathematical Soc.
Release Date : 2004
Functional Analysis written by Yuli Eidelman and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
Introduces the methods and language of functional analysis, including Hilbert spaces, Fredholm theory for compact operators and spectral theory of self-adjoint operators. This work presents the theorems and methods of abstract functional analysis and applications of these methods to Banach algebras and theory of unbounded self-adjoint operators.
History Of Functional Analysis
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Author : J. Dieudonne
language : en
Publisher: Elsevier
Release Date : 1983-01-01
History Of Functional Analysis written by J. Dieudonne and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983-01-01 with Mathematics categories.
History of Functional Analysis presents functional analysis as a rather complex blend of algebra and topology, with its evolution influenced by the development of these two branches of mathematics. The book adopts a narrower definition—one that is assumed to satisfy various algebraic and topological conditions. A moment of reflections shows that this already covers a large part of modern analysis, in particular, the theory of partial differential equations. This volume comprises nine chapters, the first of which focuses on linear differential equations and the Sturm-Liouville problem. The succeeding chapters go on to discuss the ""crypto-integral"" equations, including the Dirichlet principle and the Beer-Neumann method; the equation of vibrating membranes, including the contributions of Poincare and H.A. Schwarz's 1885 paper; and the idea of infinite dimension. Other chapters cover the crucial years and the definition of Hilbert space, including Fredholm's discovery and the contributions of Hilbert; duality and the definition of normed spaces, including the Hahn-Banach theorem and the method of the gliding hump and Baire category; spectral theory after 1900, including the theories and works of F. Riesz, Hilbert, von Neumann, Weyl, and Carleman; locally convex spaces and the theory of distributions; and applications of functional analysis to differential and partial differential equations. This book will be of interest to practitioners in the fields of mathematics and statistics.
Real And Functional Analysis
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Author : Vladimir I. Bogachev
language : en
Publisher: Springer Nature
Release Date : 2020-02-25
Real And Functional Analysis written by Vladimir I. Bogachev and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-02-25 with Mathematics categories.
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.
Functional Analysis Sobolev Spaces And Partial Differential Equations
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Author : Haim Brezis
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-11-10
Functional Analysis Sobolev Spaces And Partial Differential Equations written by Haim Brezis and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-11-10 with Mathematics categories.
This textbook is a completely revised, updated, and expanded English edition of the important Analyse fonctionnelle (1983). In addition, it contains a wealth of problems and exercises (with solutions) to guide the reader. Uniquely, this book presents in a coherent, concise and unified way the main results from functional analysis together with the main results from the theory of partial differential equations (PDEs). Although there are many books on functional analysis and many on PDEs, this is the first to cover both of these closely connected topics. Since the French book was first published, it has been translated into Spanish, Italian, Japanese, Korean, Romanian, Greek and Chinese. The English edition makes a welcome addition to this list.
A Course In Functional Analysis
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Author : John B Conway
language : en
Publisher: Springer
Release Date : 2019-03-09
A Course In Functional Analysis written by John B Conway and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-03-09 with Mathematics categories.
Functional analysis has become a sufficiently large area of mathematics that it is possible to find two research mathematicians, both of whom call themselves functional analysts, who have great difficulty understanding the work of the other. The common thread is the existence of a linear space with a topology or two (or more). Here the paths diverge in the choice of how that topology is defined and in whether to study the geometry of the linear space, or the linear operators on the space, or both. In this book I have tried to follow the common thread rather than any special topic. I have included some topics that a few years ago might have been thought of as specialized but which impress me as interesting and basic. Near the end of this work I gave into my natural temptation and included some operator theory that, though basic for operator theory, might be considered specialized by some functional analysts.
Linear Functional Analysis
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Author : Hans Wilhelm Alt
language : en
Publisher: Springer
Release Date : 2016-07-06
Linear Functional Analysis written by Hans Wilhelm Alt and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-07-06 with Mathematics categories.
This book gives an introduction to Linear Functional Analysis, which is a synthesis of algebra, topology, and analysis. In addition to the basic theory it explains operator theory, distributions, Sobolev spaces, and many other things. The text is self-contained and includes all proofs, as well as many exercises, most of them with solutions. Moreover, there are a number of appendices, for example on Lebesgue integration theory. A complete introduction to the subject, Linear Functional Analysis will be particularly useful to readers who want to quickly get to the key statements and who are interested in applications to differential equations.
A Friendly Approach To Functional Analysis
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Author : Amol Sasane
language : en
Publisher: World Scientific Publishing Company
Release Date : 2017-02-20
A Friendly Approach To Functional Analysis written by Amol Sasane and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-02-20 with Mathematics categories.
'The book is unusual among functional analysis books in devoting a lot of space to the derivative. The ‘friendly’ aspect promised in the title is not explained, but there are three things I think would strike most students as friendly: the slow pace, the enormous number of examples, and complete solutions to all the exercises.'MAA ReviewsThis book constitutes a concise introductory course on Functional Analysis for students who have studied calculus and linear algebra. The topics covered are Banach spaces, continuous linear transformations, Frechet derivative, geometry of Hilbert spaces, compact operators, and distributions. In addition, the book includes selected applications of functional analysis to differential equations, optimization, physics (classical and quantum mechanics), and numerical analysis. The book contains 197 problems, meant to reinforce the fundamental concepts. The inclusion of detailed solutions to all the exercises makes the book ideal also for self-study.A Friendly Approach to Functional Analysis is written specifically for undergraduate students of pure mathematics and engineering, and those studying joint programmes with mathematics.
Introduction To Functional Analysis
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Author : Christian Clason
language : en
Publisher: Springer Nature
Release Date : 2020-11-30
Introduction To Functional Analysis written by Christian Clason and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-30 with Mathematics categories.
Functional analysis has become one of the essential foundations of modern applied mathematics in the last decades, from the theory and numerical solution of differential equations, from optimization and probability theory to medical imaging and mathematical image processing. This textbook offers a compact introduction to the theory and is designed to be used during one semester, fitting exactly 26 lectures of 90 minutes each. It ranges from the topological fundamentals recalled from basic lectures on real analysis to spectral theory in Hilbert spaces. Special attention is given to the central results on dual spaces and weak convergence.