Functional Analysis

An Introduction to Banach Space Theory

Author: Terry J. Morrison

Publisher: John Wiley & Sons

ISBN: 1118031245

Category: Mathematics

Page: 376

View: 5879

A powerful introduction to one of the most active areas of theoretical and applied mathematics This distinctive introduction to one of the most far-reaching and beautiful areas of mathematics focuses on Banach spaces as the milieu in which most of the fundamental concepts are presented. While occasionally using the more general topological vector space and locally convex space setting, it emphasizes the development of the reader's mathematical maturity and the ability to both understand and "do" mathematics. In so doing, Functional Analysis provides a strong springboard for further exploration on the wide range of topics the book presents, including: * Weak topologies and applications * Operators on Banach spaces * Bases in Banach spaces * Sequences, series, and geometry in Banach spaces Stressing the general techniques underlying the proofs, Functional Analysis also features many exercises for immediate clarification of points under discussion. This thoughtful, well-organized synthesis of the work of those mathematicians who created the discipline of functional analysis as we know it today also provides a rich source of research topics and reference material.

Introduction to Functional Analysis

Author: Reinhold Meise,Dietmar Vogt

Publisher: Clarendon Press

ISBN: 0191590924

Category:

Page: 448

View: 7054

The book is written for students of mathematics and physics who have a basic knowledge of analysis and linear algebra. It can be used as a textbook for courses and/or seminars in functional analysis. Starting from metric spaces it proceeds quickly to the central results of the field, including the theorem of HahnBanach. The spaces (p Lp (X,(), C(X)' and Sobolov spaces are introduced. A chapter on spectral theory contains the Riesz theory of compact operators, basic facts on Banach and C*-algebras and the spectral representation for bounded normal and unbounded self-adjoint operators in Hilbert spaces. An introduction to locally convex spaces and their duality theory provides the basis for a comprehensive treatment of Fr--eacute--;chet spaces and their duals. In particular recent results on sequences spaces, linear topological invariants and short exact sequences of Fr--eacute--;chet spaces and the splitting of such sequences are presented. These results are not contained in any other book in this field.

From Vector Spaces to Function Spaces

Introduction to Functional Analysis with Applications

Author: Yutaka Yamamoto

Publisher: SIAM

ISBN: 1611972302

Category: Mathematics

Page: 260

View: 4298

A guide to analytic methods in applied mathematics from the perspective of functional analysis, suitable for scientists, engineers and students.

Functional Analysis

An Introduction to Metric Spaces, Hilbert Spaces, and Banach Algebras

Author: Joseph Muscat

Publisher: Springer

ISBN: 3319067281

Category: Mathematics

Page: 420

View: 5581

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

An Introduction

Author: Yuli Eidelman,Vitali D. Milman,Antonis Tsolomitis

Publisher: American Mathematical Soc.

ISBN: 0821836463

Category: Mathematics

Page: 322

View: 3215

The goal of this textbook is to provide an introduction to the methods and language of functional analysis, including Hilbert spaces, Fredholm theory for compact operators, and spectral theory of self-adjoint operators. It also presents the basic theorems and methods of abstract functional analysis and a few applications of these methods to Banach algebras and the theory of unbounded self-adjoint operators. The text corresponds to material for two semester courses (Part I and Part II, respectively), and it is as self-contained as possible. The only prerequisites for the first part are minimal amounts of linear algebra and calculus. However, for the second course (Part II), it is useful to have some knowledge of topology and measure theory. Each chapter is followed by numerous exercises, whose solutions are given at the end of the book.

Introductory Functional Analysis with Applications

Author: Kreyszig

Publisher: John Wiley & Sons

ISBN: 9788126511914

Category: Functional analysis

Page: 704

View: 3073

Market_Desc: · Undergraduate and Graduate Students in Mathematics and Physics· Engineering· Instructors

Introduction to Functional Analysis with Applications

Author: A. H. Siddiqi,Khalil Ahmad,Pammy Manchanda

Publisher: Anshan Pub

ISBN: 9781904798910

Category: Mathematics

Page: 362

View: 4290

As science and technology are increasingly refined and interrelated, the demand for mathematical concepts beyond vector algebra and differential and integral calculus has greatly increased. There are four fundamental theorems dealing with properties of functionals and operators called Hahn-Banach theorem, Banach-Steinhaus theorem, Open mapping theorem and Closed graph theorem. Notions of differentiability and integrability of operators are also studied in functional analysis. Applications of functional analysis to operator equations, boundary value problems, optimization, variational inequalities, finite element methods, optimal control and wavelets are all discussed at length, reflecting current trends in the study of functional analysis. This book introduces the above concepts in a way accessible to readers having minimum possible prerequisite of undergraduate mathematics.

An Introduction to Functional Analysis

Author: Charles Swartz

Publisher: CRC Press

ISBN: 9780824786434

Category: Mathematics

Page: 600

View: 2330

Based on an introductory, graduate-level course given by Swartz at New Mexico State U., this textbook, written for students with a moderate knowledge of point set topology and integration theory, explains the principles and theories of functional analysis and their applications, showing the interpla

A Course in Functional Analysis

Author: John B. Conway

Publisher: Springer Science & Business Media

ISBN: 1475738285

Category: Mathematics

Page: 406

View: 5788

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.

An Introduction to Functional Analysis in Computational Mathematics

An Introduction

Author: V.I. Lebedev

Publisher: Springer Science & Business Media

ISBN: 1461241286

Category: Mathematics

Page: 256

View: 2221

The book contains the methods and bases of functional analysis that are directly adjacent to the problems of numerical mathematics and its applications; they are what one needs for the understand ing from a general viewpoint of ideas and methods of computational mathematics and of optimization problems for numerical algorithms. Functional analysis in mathematics is now just the small visible part of the iceberg. Its relief and summit were formed under the influence of this author's personal experience and tastes. This edition in English contains some additions and changes as compared to the second edition in Russian; discovered errors and misprints had been corrected again here; to the author's distress, they jump incomprehensibly from one edition to another as fleas. The list of literature is far from being complete; just a number of textbooks and monographs published in Russian have been included. The author is grateful to S. Gerasimova for her help and patience in the complex process of typing the mathematical manuscript while the author corrected, rearranged, supplemented, simplified, general ized, and improved as it seemed to him the book's contents. The author thanks G. Kontarev for the difficult job of translation and V. Klyachin for the excellent figures.

Introduction to Operator Theory I

Elements of Functional Analysis

Author: A. Brown,C. Pearcy

Publisher: Springer Science & Business Media

ISBN: 1461299268

Category: Mathematics

Page: 476

View: 2113

This book was written expressly to serve as a textbook for a one- or two-semester introductory graduate course in functional analysis. Its (soon to be published) companion volume, Operators on Hilbert Space, is in tended to be used as a textbook for a subsequent course in operator theory. In writing these books we have naturally been concerned with the level of preparation of the potential reader, and, roughly speaking, we suppose him to be familiar with the approximate equivalent of a one-semester course in each of the following areas: linear algebra, general topology, complex analysis, and measure theory. Experience has taught us, however, that such a sequence of courses inevitably fails to treat certain topics that are important in the study of functional analysis and operator theory. For example, tensor products are frequently not discussed in a first course in linear algebra. Likewise for the topics of convergence of nets and the Baire category theorem in a course in topology, and the connections between measure and topology in a course in measure theory. For this reason we have chosen to devote the first ten chapters of this volume (entitled Part I) to topics of a preliminary nature. In other words, Part I summarizes in considerable detail what a student should (and eventually must) know in order to study functional analysis and operator theory successfully.

A First Course in Functional Analysis

Theory and Applications

Author: Rabindranath Sen

Publisher: Anthem Press

ISBN: 1783083247

Category: Mathematics

Page: 486

View: 6651

This book provides the reader with a comprehensive introduction to functional analysis. Topics include normed linear and Hilbert spaces, the Hahn-Banach theorem, the closed graph theorem, the open mapping theorem, linear operator theory, the spectral theory, and a brief introduction to the Lebesgue measure. The book explains the motivation for the development of these theories, and applications that illustrate the theories in action. Applications in optimal control theory, variational problems, wavelet analysis and dynamical systems are also highlighted. ‘A First Course in Functional Analysis’ will serve as a ready reference to students not only of mathematics, but also of allied subjects in applied mathematics, physics, statistics and engineering.

Introduction to Measure Theory and Functional Analysis

Author: Piermarco Cannarsa,Teresa D'Aprile

Publisher: Springer

ISBN: 3319170198

Category: Mathematics

Page: 314

View: 3961

This book introduces readers to theories that play a crucial role in modern mathematics, such as integration and functional analysis, employing a unifying approach that views these two subjects as being deeply intertwined. This feature is particularly evident in the broad range of problems examined, the solutions of which are often supported by generous hints. If the material is split into two courses, it can be supplemented by additional topics from the third part of the book, such as functions of bounded variation, absolutely continuous functions, and signed measures. This textbook addresses the needs of graduate students in mathematics, who will find the basic material they will need in their future careers, as well as those of researchers, who will appreciate the self-contained exposition which requires no other preliminaries than basic calculus and linear algebra.

Functional Analysis

Introduction to Further Topics in Analysis

Author: Elias M. Stein,Rami Shakarchi

Publisher: Princeton University Press

ISBN: 0691113874

Category: Mathematics

Page: 423

View: 1701

"This book covers such topics as Lp̂ spaces, distributions, Baire category, probability theory and Brownian motion, several complex variables and oscillatory integrals in Fourier analysis. The authors focus on key results in each area, highlighting their importance and the organic unity of the subject"--Provided by publisher.

An Introductory Course in Functional Analysis

Author: Adam Bowers,Nigel J. Kalton

Publisher: Springer

ISBN: 1493919458

Category: Mathematics

Page: 232

View: 7479

Based on a graduate course by the celebrated analyst Nigel Kalton, this well-balanced introduction to functional analysis makes clear not only how, but why, the field developed. All major topics belonging to a first course in functional analysis are covered. However, unlike traditional introductions to the subject, Banach spaces are emphasized over Hilbert spaces, and many details are presented in a novel manner, such as the proof of the Hahn–Banach theorem based on an inf-convolution technique, the proof of Schauder's theorem, and the proof of the Milman–Pettis theorem. With the inclusion of many illustrative examples and exercises, An Introductory Course in Functional Analysis equips the reader to apply the theory and to master its subtleties. It is therefore well-suited as a textbook for a one- or two-semester introductory course in functional analysis or as a companion for independent study.

An Introduction to Banach Space Theory

Author: Robert E. Megginson

Publisher: Springer Science & Business Media

ISBN: 1461206030

Category: Mathematics

Page: 599

View: 9707

Preparing students for further study of both the classical works and current research, this is an accessible text for students who have had a course in real and complex analysis and understand the basic properties of L p spaces. It is sprinkled liberally with examples, historical notes, citations, and original sources, and over 450 exercises provide practice in the use of the results developed in the text through supplementary examples and counterexamples.