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Linear Functional Analysis
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Book Synopsis Linear Functional Analysis by : Bryan Rynne
Download or read book Linear Functional Analysis written by Bryan Rynne and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the ideas and methods of linear func tional analysis at a level appropriate to the final year of an undergraduate course at a British university. The prerequisites for reading it are a standard undergraduate knowledge of linear algebra and real analysis (including the the ory of metric spaces). Part of the development of functional analysis can be traced to attempts to find a suitable framework in which to discuss differential and integral equa tions. Often, the appropriate setting turned out to be a vector space of real or complex-valued functions defined on some set. In general, such a vector space is infinite-dimensional. This leads to difficulties in that, although many of the elementary properties of finite-dimensional vector spaces hold in infinite dimensional vector spaces, many others do not. For example, in general infinite dimensional vector spaces there is no framework in which to make sense of an alytic concepts such as convergence and continuity. Nevertheless, on the spaces of most interest to us there is often a norm (which extends the idea of the length of a vector to a somewhat more abstract setting). Since a norm on a vector space gives rise to a metric on the space, it is now possible to do analysis in the space. As real or complex-valued functions are often called functionals, the term functional analysis came to be used for this topic. We now briefly outline the contents of the book.
Book Synopsis Linear Functional Analysis by : Hans Wilhelm Alt
Download or read book Linear Functional Analysis written by Hans Wilhelm Alt and published by Springer. This book was released on 2016-07-06 with total page 435 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Basic Methods of Linear Functional Analysis by : John D. Pryce
Download or read book Basic Methods of Linear Functional Analysis written by John D. Pryce and published by Courier Corporation. This book was released on 2014-05-05 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to the themes of mathematical analysis, geared toward advanced undergraduate and graduate students. Topics include operators, function spaces, Hilbert spaces, and elementary Fourier analysis. Numerous exercises and worked examples.1973 edition.
Book Synopsis Linear Functional Analysis by : Joan Cerda
Download or read book Linear Functional Analysis written by Joan Cerda and published by American Mathematical Soc.. This book was released on 2010 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents the basic facts of linear functional analysis as related to fundamental aspects of mathematical analysis and their applications. It avoids unnecessary terminology and generality and focuses on showing how the knowledge of these structures clarifies what is essential in analytic problems. The presentation is intended to be accessible to readers whose backgrounds include basic linear algebra, integration theory, and general topology.
Book Synopsis Linear and Nonlinear Functional Analysis with Applications by : Philippe G. Ciarlet
Download or read book Linear and Nonlinear Functional Analysis with Applications written by Philippe G. Ciarlet and published by SIAM. This book was released on 2013-10-10 with total page 847 pages. Available in PDF, EPUB and Kindle. Book excerpt: This single-volume textbook covers the fundamentals of linear and nonlinear functional analysis, illustrating most of the basic theorems with numerous applications to linear and nonlinear partial differential equations and to selected topics from numerical analysis and optimization theory. This book has pedagogical appeal because it features self-contained and complete proofs of most of the theorems, some of which are not always easy to locate in the literature or are difficult to reconstitute. It also offers 401 problems and 52 figures, plus historical notes and many original references that provide an idea of the genesis of the important results, and it covers most of the core topics from functional analysis.
Book Synopsis Lecture Notes on Functional Analysis by : Alberto Bressan
Download or read book Lecture Notes on Functional Analysis written by Alberto Bressan and published by American Mathematical Soc.. This book was released on 2013 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is addressed to graduate students in mathematics or other disciplines who wish to understand the essential concepts of functional analysis and their applications to partial differential equations. The book is intentionally concise, presenting all the fundamental concepts and results but omitting the more specialized topics. Enough of the theory of Sobolev spaces and semigroups of linear operators is included as needed to develop significant applications to elliptic, parabolic, and hyperbolic PDEs. Throughout the book, care has been taken to explain the connections between theorems in functional analysis and familiar results of finite-dimensional linear algebra. The main concepts and ideas used in the proofs are illustrated with a large number of figures. A rich collection of homework problems is included at the end of most chapters. The book is suitable as a text for a one-semester graduate course.
Book Synopsis Functional Analysis by : R.E. Edwards
Download or read book Functional Analysis written by R.E. Edwards and published by Courier Corporation. This book was released on 2012-10-25 with total page 802 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The book contains an enormous amount of information — mathematical, bibliographical and historical — interwoven with some outstanding heuristic discussions." — Mathematical Reviews. In this massive graduate-level study, Emeritus Professor Edwards (Australian National University, Canberra) presents a balanced account of both the abstract theory and the applications of linear functional analysis. Written for readers with a basic knowledge of set theory, general topology, and vector spaces, the book includes an abundance of carefully chosen illustrative examples and excellent exercises at the end of each chapter. Beginning with a chapter of preliminaries on set theory and topology, Dr. Edwards then presents detailed, in-depth discussions of vector spaces and topological vector spaces, the Hahn-Banach theorem (including applications to potential theory, approximation theory, game theory, and other fields) and fixed-point theorems. Subsequent chapters focus on topological duals of certain spaces: radon measures, distribution and linear partial differential equations, open mapping and closed graph theorems, boundedness principles, duality theory, the theory of compact operators and the Krein-Milman theorem and its applications to commutative harmonic analysis. Clearly and concisely written, Dr. Edwards's book offers rewarding reading to mathematicians and physicists with an interest in the important field of functional analysis. Because of the broad scope of its coverage, this volume will be especially valuable to the reader with a basic knowledge of functional analysis who wishes to learn about parts of the subject other than his own specialties. A comprehensive 32-page bibliography supplies a rich source of references to the basic literature.
Book Synopsis Functional Analysis by : Kosaku Yosida
Download or read book Functional Analysis written by Kosaku Yosida and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Introductory Functional Analysis with Applications by : Erwin Kreyszig
Download or read book Introductory Functional Analysis with Applications written by Erwin Kreyszig and published by John Wiley & Sons. This book was released on 1991-01-16 with total page 706 pages. Available in PDF, EPUB and Kindle. Book excerpt: KREYSZIG The Wiley Classics Library consists of selected books originally published by John Wiley & Sons that have become recognized classics in their respective fields. With these new unabridged and inexpensive editions, Wiley hopes to extend the life of these important works by making them available to future generations of mathematicians and scientists. Currently available in the Series: Emil Artin Geometnc Algebra R. W. Carter Simple Groups Of Lie Type Richard Courant Differential and Integrai Calculus. Volume I Richard Courant Differential and Integral Calculus. Volume II Richard Courant & D. Hilbert Methods of Mathematical Physics, Volume I Richard Courant & D. Hilbert Methods of Mathematical Physics. Volume II Harold M. S. Coxeter Introduction to Modern Geometry. Second Edition Charles W. Curtis, Irving Reiner Representation Theory of Finite Groups and Associative Algebras Nelson Dunford, Jacob T. Schwartz unear Operators. Part One. General Theory Nelson Dunford. Jacob T. Schwartz Linear Operators, Part Two. Spectral Theory—Self Adjant Operators in Hilbert Space Nelson Dunford, Jacob T. Schwartz Linear Operators. Part Three. Spectral Operators Peter Henrici Applied and Computational Complex Analysis. Volume I—Power Senes-lntegrauon-Contormal Mapping-Locatvon of Zeros Peter Hilton, Yet-Chiang Wu A Course in Modern Algebra Harry Hochstadt Integral Equations Erwin Kreyszig Introductory Functional Analysis with Applications P. M. Prenter Splines and Variational Methods C. L. Siegel Topics in Complex Function Theory. Volume I —Elliptic Functions and Uniformizatton Theory C. L. Siegel Topics in Complex Function Theory. Volume II —Automorphic and Abelian Integrals C. L. Siegel Topics In Complex Function Theory. Volume III —Abelian Functions & Modular Functions of Several Variables J. J. Stoker Differential Geometry
Book Synopsis Functional Analysis by : Theo Bühler
Download or read book Functional Analysis written by Theo Bühler and published by American Mathematical Soc.. This book was released on 2018-08-08 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: It begins in Chapter 1 with an introduction to the necessary foundations, including the Arzelà–Ascoli theorem, elementary Hilbert space theory, and the Baire Category Theorem. Chapter 2 develops the three fundamental principles of functional analysis (uniform boundedness, open mapping theorem, Hahn–Banach theorem) and discusses reflexive spaces and the James space. Chapter 3 introduces the weak and weak topologies and includes the theorems of Banach–Alaoglu, Banach–Dieudonné, Eberlein–Šmulyan, Kre&ibreve;n–Milman, as well as an introduction to topological vector spaces and applications to ergodic theory. Chapter 4 is devoted to Fredholm theory. It includes an introduction to the dual operator and to compact operators, and it establishes the closed image theorem. Chapter 5 deals with the spectral theory of bounded linear operators. It introduces complex Banach and Hilbert spaces, the continuous functional calculus for self-adjoint and normal operators, the Gelfand spectrum, spectral measures, cyclic vectors, and the spectral theorem. Chapter 6 introduces unbounded operators and their duals. It establishes the closed image theorem in this setting and extends the functional calculus and spectral measure to unbounded self-adjoint operators on Hilbert spaces. Chapter 7 gives an introduction to strongly continuous semigroups and their infinitesimal generators. It includes foundational results about the dual semigroup and analytic semigroups, an exposition of measurable functions with values in a Banach space, and a discussion of solutions to the inhomogeneous equation and their regularity properties. The appendix establishes the equivalence of the Lemma of Zorn and the Axiom of Choice, and it contains a proof of Tychonoff's theorem. With 10 to 20 elaborate exercises at the end of each chapter, this book can be used as a text for a one-or-two-semester course on functional analysis for beginning graduate students. Prerequisites are first-year analysis and linear algebra, as well as some foundational material from the second-year courses on point set topology, complex analysis in one variable, and measure and integration.
Book Synopsis Applied Algebra and Functional Analysis by : Anthony N. Michel
Download or read book Applied Algebra and Functional Analysis written by Anthony N. Michel and published by Courier Corporation. This book was released on 1993-01-01 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: "A valuable reference." — American Scientist. Excellent graduate-level treatment of set theory, algebra and analysis for applications in engineering and science. Fundamentals, algebraic structures, vector spaces and linear transformations, metric spaces, normed spaces and inner product spaces, linear operators, more. A generous number of exercises have been integrated into the text. 1981 edition.
Book Synopsis Measure, Integration & Real Analysis by : Sheldon Axler
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/
Book Synopsis Elementary Functional Analysis by : Georgi E. Shilov
Download or read book Elementary Functional Analysis written by Georgi E. Shilov and published by Courier Corporation. This book was released on 2013-04-15 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introductory text covers basic structures of mathematical analysis (linear spaces, metric spaces, normed linear spaces, etc.), differential equations, orthogonal expansions, Fourier transforms, and more. Includes problems with hints and answers. Bibliography. 1974 edition.
Book Synopsis A Course in Functional Analysis by : John B Conway
Download or read book A Course in Functional Analysis written by John B Conway and published by Springer. This book was released on 2019-03-09 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introductory text in functional analysis. Unlike many modern treatments, it begins with the particular and works its way to the more general. From the reviews: "This book is an excellent text for a first graduate course in functional analysis....Many interesting and important applications are included....It includes an abundance of exercises, and is written in the engaging and lucid style which we have come to expect from the author." --MATHEMATICAL REVIEWS
Book Synopsis Functional Analysis and Control Theory by : S. Rolewicz
Download or read book Functional Analysis and Control Theory written by S. Rolewicz and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 539 pages. Available in PDF, EPUB and Kindle. Book excerpt: Approach your problems from the right It isn't that they can't see the solution. end and begin with the answers. Then, It is that they can't see the problem. one day, perhaps you will find the final G.K. Chesterton, The Scandal of Fa question. ther Brown 'The point of a Pin'. 'The Hermit Clad in Crane Feathers' in R. Van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of mono graphs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, cod ing theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical pro gramming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces.
Book Synopsis Functional Analysis, Sobolev Spaces and Partial Differential Equations by : Haim Brezis
Download or read book Functional Analysis, Sobolev Spaces and Partial Differential Equations written by Haim Brezis and published by Springer Science & Business Media. This book was released on 2010-11-02 with total page 600 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Linear Analysis written by Bila Bollobás and published by Cambridge University Press. This book was released on 1990-11-29 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to functional analysis is intended for advanced undergraduate students, typically final year, who have some background in real analysis. The author's aim is not to cover the standard material in a standard way, but to present results of applications in contemporary mathematics and to show the relevance of functional analysis to other areas. Unusual topics covered include geometry of finite-dimensional spaces, invariant subspace, fixed-point theorem, and the Bishop-Phelps theorem. An outstanding set of exercises run from the elementary to the challenging.
