Download or read book Topics in Functional Analysis and Applications written by S. KESAVAN and published by . This book was released on 2020-11 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: Key Features:Basic knowledge in functional analysis is a pre-requisite. Illustrations via partial differential equations of physics provided. Exercises given in each chapter to augment concepts and theorems.About the Book:The book, written to give a fairly comprehensive treatment of the techniques from Functional Analysis used in the modern theory of Partial Differential Equations, is now in its third edition. The original structure of the book has been retained but each chapter has been revamped. Proofs of several theorems have been either simplified or elaborated in order to achieve greater clarity. It is hoped that this version is even more user-friendly than before. In the chapter on Distributions, some additional results, with proof, have been presented. The section on Convolution of Functions has been rewritten. In the chapter on Sobolev Spaces, the section containing Stampacchia's theorem on composition of functions has been reorganized. Some additional results on Eigenvalue problems are presented. The material in the text is supplemented by four appendices and updated bibliography at the end.
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.
Download or read book Topics in Functional Analysis and Applications written by S. Kesavan and published by New Age International. This book was released on 1989 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Aim Of This Book Is To Give A Fairly Complete, Yet Simple, Treatment Of The Techniques From Functional Analysis Used In The Modern Theory Of Partial Differential Equations And Illustrate Their Applications Via Examples. The Book Provides An Introduction To The Theory Of Distributions, Sobolev Spaces And Semigroups And The Results Are Applied To The Study Of Weak Solutions Of Elliptic Boundary Value Problems And Evolution Equations. It Also Contains An Introduction To Some Techniques In Nonlinear Analysis And Touches Upon Some Of The Frontiers Of Current Research In That Area.The Material In The Text Is Supplemented By Four Appendices, Bibliographic Comments At The End Of Each Chapter And Several Exercises. These Exercises Are Fully Solved In A Companion Volume. This Book Should Be Of Use Both As A Text-Book And As A Source Of Reference For Research Workers In The Area.
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
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.
Download or read book Functional Analysis Spectral Theory and Applications written by Manfred Einsiedler and published by Springer. This book was released on 2017-11-21 with total page 614 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides a careful treatment of functional analysis and some of its applications in analysis, number theory, and ergodic theory. In addition to discussing core material in functional analysis, the authors cover more recent and advanced topics, including Weyl’s law for eigenfunctions of the Laplace operator, amenability and property (T), the measurable functional calculus, spectral theory for unbounded operators, and an account of Tao’s approach to the prime number theorem using Banach algebras. The book further contains numerous examples and exercises, making it suitable for both lecture courses and self-study. Functional Analysis, Spectral Theory, and Applications is aimed at postgraduate and advanced undergraduate students with some background in analysis and algebra, but will also appeal to everyone with an interest in seeing how functional analysis can be applied to other parts of mathematics.
Download or read book Operator Theory Functional Analysis and Applications written by M. Amélia Bastos and published by Springer Nature. This book was released on 2021-03-31 with total page 654 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents 30 articles on the topic areas discussed at the 30th “International Workshop on Operator Theory and its Applications”, held in Lisbon in July 2019. The contributions include both expository essays and original research papers reflecting recent advances in the traditional IWOTA areas and emerging adjacent fields, as well as the applications of Operator Theory and Functional Analysis. The topics range from C*–algebras and Banach *–algebras, Sturm-Liouville theory, integrable systems, dilation theory, frame theory, Toeplitz, Hankel, and singular integral operators, to questions from lattice, group and matrix theories, complex analysis, harmonic analysis, and function spaces. Given its scope, the book is chiefly intended for researchers and graduate students in the areas of Operator Theory, Functional Analysis, their applications and adjacent fields.
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 265 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.
Download or read book Functional Analysis written by Michel Willem and published by Springer Nature. This book was released on 2023-01-27 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook presents the principles of functional analysis in a clear and concise way. The first three chapters describe the general notions of distance, integral, and norm, as well as their relations. Fundamental examples are provided in the three chapters that follow: Lebesgue spaces, dual spaces, and Sobolev spaces. Two subsequent chapters develop applications to capacity theory and elliptic problems. In particular, the isoperimetric inequality and the Pólya-Szegő and Faber-Krahn inequalities are proved by purely functional methods. The epilogue contains a sketch of the history of functional analysis in relation to integration and differentiation. Starting from elementary analysis and introducing relevant research, this work is an excellent resource for students in mathematics and applied mathematics. The second edition of Functional Analysis includes several improvements as well as the addition of supplementary material. Specifically, the coverage of advanced calculus and distribution theory has been completely rewritten and expanded. New proofs, theorems, and applications have been added as well for readers to explore.
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 446 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.
Download or read book Applied Functional Analysis written by Eberhard Zeidler and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 503 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first part of a self-contained, elementary textbook, combining linear functional analysis, nonlinear functional analysis, numerical functional analysis, and their substantial applications with each other. As such, the book addresses undergraduate students and beginning graduate students of mathematics, physics, and engineering who want to learn how functional analysis elegantly solves mathematical problems which relate to our real world. Applications concern ordinary and partial differential equations, the method of finite elements, integral equations, special functions, both the Schroedinger approach and the Feynman approach to quantum physics, and quantum statistics. As a prerequisite, readers should be familiar with some basic facts of calculus. The second part has been published under the title, Applied Functional Analysis: Main Principles and Their Applications.
Download or read book Descriptive Topology in Selected Topics of Functional Analysis written by Jerzy Kąkol and published by Springer Science & Business Media. This book was released on 2011-08-30 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Descriptive Topology in Selected Topics of Functional Analysis" is a collection of recent developments in the field of descriptive topology, specifically focused on the classes of infinite-dimensional topological vector spaces that appear in functional analysis. Such spaces include Fréchet spaces, (LF)-spaces and their duals, and the space of continuous real-valued functions C(X) on a completely regular Hausdorff space X, to name a few. These vector spaces appear in functional analysis in distribution theory, differential equations, complex analysis, and various other analytical settings. This monograph provides new insights into the connections between the topological properties of linear function spaces and their applications in functional analysis.
Download or read book Geometric Functional Analysis and its Applications written by R. B. Holmes and published by Springer. This book was released on 2012-12-12 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book has evolved from my experience over the past decade in teaching and doing research in functional analysis and certain of its appli cations. These applications are to optimization theory in general and to best approximation theory in particular. The geometric nature of the subjects has greatly influenced the approach to functional analysis presented herein, especially its basis on the unifying concept of convexity. Most of the major theorems either concern or depend on properties of convex sets; the others generally pertain to conjugate spaces or compactness properties, both of which topics are important for the proper setting and resolution of optimization problems. In consequence, and in contrast to most other treatments of functional analysis, there is no discussion of spectral theory, and only the most basic and general properties of linear operators are established. Some of the theoretical highlights of the book are the Banach space theorems associated with the names of Dixmier, Krein, James, Smulian, Bishop-Phelps, Brondsted-Rockafellar, and Bessaga-Pelczynski. Prior to these (and others) we establish to two most important principles of geometric functional analysis: the extended Krein-Milman theorem and the Hahn Banach principle, the latter appearing in ten different but equivalent formula tions (some of which are optimality criteria for convex programs). In addition, a good deal of attention is paid to properties and characterizations of conjugate spaces, especially reflexive spaces.
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:
Download or read book Functional Analysis written by S. Kesavan and published by Springer. This book was released on 2009-01-15 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: The material presented in this book is suited for a first course in Functional Analysis which can be followed by Masters students. While covering all the standard material expected of such a course, efforts have been made to illustrate the use of various theorems via examples taken from differential equations and the calculus of variations, either through brief sections or through exercises. In fact, this book will be particularly useful for students who would like to pursue a research career in the applications of mathematics. The book includes a chapter on weak and weak topologies and their applications to the notions of reflexivity, separability and uniform convexity. The chapter on the Lebesgue spaces also presents the theory of one of the simplest classes of Sobolev spaces. The book includes a chapter on compact operators and the spectral theory for compact self-adjoint operators on a Hilbert space. Each chapter has large collection of exercises at the end. These illustrate the results of the text, show the optimality of the hypotheses of various theorems via examples or counterexamples, or develop simple versions of theories not elaborated upon in the text.
Download or read book Essential Results of Functional Analysis written by Robert J. Zimmer and published by University of Chicago Press. This book was released on 1990-01-15 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt: Functional analysis is a broad mathematical area with strong connections to many domains within mathematics and physics. This book, based on a first-year graduate course taught by Robert J. Zimmer at the University of Chicago, is a complete, concise presentation of fundamental ideas and theorems of functional analysis. It introduces essential notions and results from many areas of mathematics to which functional analysis makes important contributions, and it demonstrates the unity of perspective and technique made possible by the functional analytic approach. Zimmer provides an introductory chapter summarizing measure theory and the elementary theory of Banach and Hilbert spaces, followed by a discussion of various examples of topological vector spaces, seminorms defining them, and natural classes of linear operators. He then presents basic results for a wide range of topics: convexity and fixed point theorems, compact operators, compact groups and their representations, spectral theory of bounded operators, ergodic theory, commutative C*-algebras, Fourier transforms, Sobolev embedding theorems, distributions, and elliptic differential operators. In treating all of these topics, Zimmer's emphasis is not on the development of all related machinery or on encyclopedic coverage but rather on the direct, complete presentation of central theorems and the structural framework and examples needed to understand them. Sets of exercises are included at the end of each chapter. For graduate students and researchers in mathematics who have mastered elementary analysis, this book is an entrée and reference to the full range of theory and applications in which functional analysis plays a part. For physics students and researchers interested in these topics, the lectures supply a thorough mathematical grounding.
Download or read book Functional Analysis written by Peter D. Lax and published by John Wiley & Sons. This book was released on 2014-08-28 with total page 451 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
