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Functional Analysis

Functional Analysis Book
Author : Kösaku Yosida
Publisher : Springer Science & Business Media
Release : 2012-12-06
ISBN : 3642618596
Language : En, Es, Fr & De

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Book Description :

The present book is based on lectures given by the author at the University of Tokyo during the past ten years. It is intended as a textbook to be studied by students on their own or to be used in a course on Functional Analysis, i. e. , the general theory of linear operators in function spaces together with salient features of its application to diverse fields of modern and classical analysis. Necessary prerequisites for the reading of this book are summarized, with or without proof, in Chapter 0 under titles: Set Theory, Topo logical Spaces, Measure Spaces and Linear Spaces. Then, starting with the chapter on Semi-norms, a general theory of Banach and Hilbert spaces is presented in connection with the theory of generalized functions of S. L. SOBOLEV and L. SCHWARTZ. While the book is primarily addressed to graduate students, it is hoped it might prove useful to research mathe maticians, both pure and applied. The reader may pass, e. g. , from Chapter IX (Analytical Theory of Semi-groups) directly to Chapter XIII (Ergodic Theory and Diffusion Theory) and to Chapter XIV (Integration of the Equation of Evolution). Such materials as "Weak Topologies and Duality in Locally Convex Spaces" and "Nuclear Spaces" are presented in the form of the appendices to Chapter V and Chapter X, respectively. These might be skipped for the first reading by those who are interested rather in the application of linear operators.

Introductory Functional Analysis with Applications

Introductory Functional Analysis with Applications Book
Author : Erwin Kreyszig
Publisher : John Wiley & Sons
Release : 1991-01-16
ISBN : 0471504599
Language : En, Es, Fr & De

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Book Description :

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

A Course in Functional Analysis

A Course in Functional Analysis Book
Author : John B. Conway
Publisher : Springer Science & Business Media
Release : 1994-01-25
ISBN : 9780387972459
Language : En, Es, Fr & De

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Book Description :

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

Functional Analysis

Functional Analysis Book
Author : Joseph Muscat
Publisher : Springer
Release : 2014-07-23
ISBN : 3319067281
Language : En, Es, Fr & De

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Book Description :

This textbook is an introduction to functional analysis suited to final year undergraduates or beginning graduates. Its various applications of Hilbert spaces, including least squares approximation, inverse problems, and Tikhonov regularization, should appeal not only to mathematicians interested in applications, but also to researchers in related fields. Functional Analysis adopts a self-contained approach to Banach spaces and operator theory that covers the main topics, based upon the classical sequence and function spaces and their operators. It assumes only a minimum of knowledge in elementary linear algebra and real analysis; the latter is redone in the light of metric spaces. It contains more than a thousand worked examples and exercises, which make up the main body of the book.

Functional Analysis and Linear Control Theory

Functional Analysis and Linear Control Theory Book
Author : J. R. Leigh
Publisher : Courier Corporation
Release : 2007-03-16
ISBN : 048645813X
Language : En, Es, Fr & De

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Book Description :

Originally published: London; New York: Academic Press, 1980, in series: Mathematics in science and engineering; v. 156.

Functional Analysis

Functional Analysis Book
Author : Robert E. Edwards
Publisher : Courier Corporation
Release : 1995-01-01
ISBN : 9780486681436
Language : En, Es, Fr & De

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Book Description :

Massive compilation offers detailed, in-depth discussions of vector spaces, Hahn-Banach theorem, fixed-point theorems, duality theory, Krein-Milman theorem, theory of compact operators, much more. Many examples and exercises. 32-page bibliography. 1965 edition.

A Friendly Approach to Functional Analysis

A Friendly Approach to Functional Analysis Book
Author : Amol Sasane
Publisher : World Scientific Publishing Company
Release : 2017-02-20
ISBN : 1786343363
Language : En, Es, Fr & De

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Book Description :

This 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. Request Inspection Copy

Functional Analysis Calculus of Variations and Optimal Control

Functional Analysis  Calculus of Variations and Optimal Control Book
Author : Francis Clarke
Publisher : Springer Science & Business Media
Release : 2013-02-06
ISBN : 1447148207
Language : En, Es, Fr & De

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Book Description :

Functional analysis owes much of its early impetus to problems that arise in the calculus of variations. In turn, the methods developed there have been applied to optimal control, an area that also requires new tools, such as nonsmooth analysis. This self-contained textbook gives a complete course on all these topics. It is written by a leading specialist who is also a noted expositor. This book provides a thorough introduction to functional analysis and includes many novel elements as well as the standard topics. A short course on nonsmooth analysis and geometry completes the first half of the book whilst the second half concerns the calculus of variations and optimal control. The author provides a comprehensive course on these subjects, from their inception through to the present. A notable feature is the inclusion of recent, unifying developments on regularity, multiplier rules, and the Pontryagin maximum principle, which appear here for the first time in a textbook. Other major themes include existence and Hamilton-Jacobi methods. The many substantial examples, and the more than three hundred exercises, treat such topics as viscosity solutions, nonsmooth Lagrangians, the logarithmic Sobolev inequality, periodic trajectories, and systems theory. They also touch lightly upon several fields of application: mechanics, economics, resources, finance, control engineering. Functional Analysis, Calculus of Variations and Optimal Control is intended to support several different courses at the first-year or second-year graduate level, on functional analysis, on the calculus of variations and optimal control, or on some combination. For this reason, it has been organized with customization in mind. The text also has considerable value as a reference. Besides its advanced results in the calculus of variations and optimal control, its polished presentation of certain other topics (for example convex analysis, measurable selections, metric regularity, and nonsmooth analysis) will be appreciated by researchers in these and related fields.

History of Functional Analysis

History of Functional Analysis Book
Author : J. Dieudonne
Publisher : Elsevier
Release : 1983-01-01
ISBN : 9780080871608
Language : En, Es, Fr & De

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Book Description :

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.

Functional Analysis in Mechanics

Functional Analysis in Mechanics Book
Author : Leonid P. Lebedev,Iosif I. Vorovich,Michael J. Cloud
Publisher : Springer Science & Business Media
Release : 2012-10-23
ISBN : 1461458684
Language : En, Es, Fr & De

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Book Description :

This book offers a brief, practically complete, and relatively simple introduction to functional analysis. It also illustrates the application of functional analytic methods to the science of continuum mechanics. Abstract but powerful mathematical notions are tightly interwoven with physical ideas in the treatment of nontrivial boundary value problems for mechanical objects. This second edition includes more extended coverage of the classical and abstract portions of functional analysis. Taken together, the first three chapters now constitute a regular text on applied functional analysis. This potential use of the book is supported by a significantly extended set of exercises with hints and solutions. A new appendix, providing a convenient listing of essential inequalities and imbedding results, has been added. The book should appeal to graduate students and researchers in physics, engineering, and applied mathematics. Reviews of first edition: "This book covers functional analysis and its applications to continuum mechanics. The presentation is concise but complete, and is intended for readers in continuum mechanics who wish to understand the mathematical underpinnings of the discipline. ... Detailed solutions of the exercises are provided in an appendix." (L’Enseignment Mathematique, Vol. 49 (1-2), 2003) "The reader comes away with a profound appreciation both of the physics and its importance, and of the beauty of the functional analytic method, which, in skillful hands, has the power to dissolve and clarify these difficult problems as peroxide does clotted blood. Numerous exercises ... test the reader’s comprehension at every stage. Summing Up: Recommended." (F. E. J. Linton, Choice, September, 2003)

Functional Analysis

Functional Analysis Book
Author : Peter D. Lax
Publisher : John Wiley & Sons
Release : 2014-08-28
ISBN : 1118626745
Language : En, Es, Fr & De

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Book Description :

Includes sections on the spectral resolution and spectralrepresentation of self adjoint operators, invariant subspaces,strongly continuous one-parameter semigroups, the index ofoperators, 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 realvariables. * Includes an appendix on the Riesz representation theorem.

Linear Functional Analysis

Linear Functional Analysis Book
Author : Bryan P. Rynne,Martin A. Youngson
Publisher : Springer Science & Business Media
Release : 2000
ISBN : 1852332573
Language : En, Es, Fr & De

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Book Description :

This introduction to the ideas and methods of linear functional analysis shows how familiar and useful concepts from finite-dimensional linear algebra can be extended or generalized to infinite-dimensional spaces. Aimed at advanced undergraduates in mathematics and physics, the book assumes a standard background of linear algebra, real analysis (including the theory of metric spaces), and Lebesgue integration, although an introductory chapter summarizes the requisite material. The initial chapters develop the theory of infinite-dimensional normed spaces, in particular Hilbert spaces, after which the emphasis shifts to studying operators between such spaces. Functional analysis has applications to a vast range of areas of mathematics; the final chapters discuss the particularly important areas of integral and differential equations. Further highlights of the second edition include: a new chapter on the Hahn-Banach theorem and its applications to the theory of duality. This chapter also introduces the basic properties of projection operators on Banach spaces, and weak convergence of sequences in Banach spaces - topics that have applications to both linear and nonlinear functional analysis; extended coverage of the uniform boundedness theorem; plenty of exercises, with solutions provided at the back of the book.

Functional Analysis in Mechanics

Functional Analysis in Mechanics Book
Author : Leonid P. Lebedev,I. I. Vorovich
Publisher : Springer Science & Business Media
Release : 2002-11-20
ISBN : 0387955194
Language : En, Es, Fr & De

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Book Description :

This is a self-contained book that covers the foundations of functional analysis while introducing the essential topics of the chosen applications. Graduate level students in mathematics and engineering will find the text useful.

Introduction to Functional Analysis

Introduction to Functional Analysis Book
Author : Christian Clason
Publisher : Birkhäuser
Release : 2020-12-01
ISBN : 9783030527839
Language : En, Es, Fr & De

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Book Description :

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.

Functional Analysis

Functional Analysis Book
Author : P. K. Jain,Khalil Ahmad,Om P. Ahuja
Publisher : New Age International
Release : 1995
ISBN : 9788122408010
Language : En, Es, Fr & De

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Book Description :

The Book Is Intended To Serve As A Textbook For An Introductory Course In Functional Analysis For The Senior Undergraduate And Graduate Students. It Can Also Be Useful For The Senior Students Of Applied Mathematics, Statistics, Operations Research, Engineering And Theoretical Physics. The Text Starts With A Chapter On Preliminaries Discussing Basic Concepts And Results Which Would Be Taken For Granted Later In The Book. This Is Followed By Chapters On Normed And Banach Spaces, Bounded Linear Operators, Bounded Linear Functionals. The Concept And Specific Geometry Of Hilbert Spaces, Functionals And Operators On Hilbert Spaces And Introduction To Spectral Theory. An Appendix Has Been Given On Schauder Bases.The Salient Features Of The Book Are: * Presentation Of The Subject In A Natural Way * Description Of The Concepts With Justification * Clear And Precise Exposition Avoiding Pendantry * Various Examples And Counter Examples * Graded Problems Throughout Each ChapterNotes And Remarks Within The Text Enhances The Utility Of The Book For The Students.

Aspects of Positivity in Functional Analysis

Aspects of Positivity in Functional Analysis Book
Author : R. Nagel,U. Schlotterbeck,M.P.H. Wolff
Publisher : Elsevier
Release : 2011-10-10
ISBN : 9780080872339
Language : En, Es, Fr & De

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Book Description :

The contributions collected in this volume exhibit the increasingly wide spectrum of applications of abstract order theory in analysis and show the possibilities of order-theoretical argumentation. The following areas are discussed: potential theory, partial differential operators of second order, Schrodinger operators, theory of convexity, one-parameter semigroups, Lie algebras, Markov processes, operator-algebras, noncommutative integration and geometry of Banach spaces.

A First Course in Functional Analysis

A First Course in Functional Analysis Book
Author : Martin Davis
Publisher : Courier Corporation
Release : 2013-05-27
ISBN : 0486315819
Language : En, Es, Fr & De

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Book Description :

Designed for undergraduate mathematics majors, this self-contained exposition of Gelfand's proof of Wiener's theorem explores set theoretic preliminaries, normed linear spaces and algebras, functions on Banach spaces, homomorphisms on normed linear spaces, and more. 1966 edition.

Functional Analysis for Probability and Stochastic Processes

Functional Analysis for Probability and Stochastic Processes Book
Author : Adam Bobrowski
Publisher : Cambridge University Press
Release : 2005-08-11
ISBN : 9780521831666
Language : En, Es, Fr & De

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Book Description :

This text presents selected areas of functional analysis that can facilitate an understanding of ideas in probability and stochastic processes. Topics covered include basic Hilbert and Banach spaces, weak topologies and Banach algebras, and the theory ofsemigroups of bounded linear operators.

Functional Analysis

Functional Analysis Book
Author : S. Kesavan
Publisher : Springer
Release : 2009-01-15
ISBN : 9386279428
Language : En, Es, Fr & De

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Book Description :

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.

Applied Functional Analysis

Applied Functional Analysis Book
Author : Eberhard Zeidler
Publisher : Springer Science & Business Media
Release : 2012-12-06
ISBN : 1461208211
Language : En, Es, Fr & De

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Book Description :

The second part of an elementary textbook which combines linear functional analysis, nonlinear functional analysis, and their substantial applications. The book addresses undergraduates and beginning graduates of mathematics, physics, and engineering who want to learn how functional analysis elegantly solves mathematical problems which relate to our real world and which play an important role in the history of mathematics. The books approach is to attempt to determine the most important applications. These concern integral equations, differential equations, bifurcation theory, the moment problem, Cebysev approximation, the optimal control of rockets, game theory, symmetries and conservation laws, the quark model, and gauge theory in elementary particle physics. The presentation is self-contained and requires only that readers be familiar with some basic facts of calculus.