Introduction to Functional Analysis

The book is written for students of mathematics and physics who have a basic knowledge of analysis and linear algebra.

Author: Reinhold Meise

Publisher: Clarendon Press

ISBN: 9780191590924

Category:

Page: 448

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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.
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Introductory Functional Analysis with Applications

Provides avenues for applying functional analysis to the practical study of natural sciences as well as mathematics.

Author: Erwin Kreyszig

Publisher: John Wiley & Sons

ISBN: 9780471504597

Category: Mathematics

Page: 704

View: 416

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Provides avenues for applying functional analysis to the practical study of natural sciences as well as mathematics. Contains worked problems on Hilbert space theory and on Banach spaces and emphasizes concepts, principles, methods and major applications of functional analysis.
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Introductory Functional Analysis

Providing an introduction to functional analysis, this text treats in detail its application to boundary-value problems and finite elements, and is distinguished by the fact that abstract concepts are motivated and illustrated wherever ...

Author: B.D. Reddy

Publisher: Springer Science & Business Media

ISBN: 9780387983073

Category: Computers

Page: 471

View: 641

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Providing an introduction to functional analysis, this text treats in detail its application to boundary-value problems and finite elements, and is distinguished by the fact that abstract concepts are motivated and illustrated wherever possible. It is intended for use by senior undergraduates and graduates in mathematics, the physical sciences and engineering, who may not have been exposed to the conventional prerequisites for a course in functional analysis, such as real analysis. Mature researchers wishing to learn the basic ideas of functional analysis will equally find this useful. Offers a good grounding in those aspects of functional analysis which are most relevant to a proper understanding and appreciation of the mathematical aspects of boundary-value problems and the finite element method.
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An Introduction to Functional Analysis

Accessible text covering core functional analysis topics in Hilbert and Banach spaces, with detailed proofs and 200 fully-worked exercises.

Author: James C. Robinson

Publisher: Cambridge University Press

ISBN: 9780521899642

Category: Mathematics

Page: 432

View: 120

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Accessible text covering core functional analysis topics in Hilbert and Banach spaces, with detailed proofs and 200 fully-worked exercises.
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Introduction to Functional Analysis

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 ...

Author: Christian Clason

Publisher: Birkhäuser

ISBN: 3030527832

Category: Mathematics

Page: 170

View: 214

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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.
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An Introductory Course in Functional Analysis

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.

Author: Adam Bowers

Publisher: Springer

ISBN: 9781493919451

Category: Mathematics

Page: 232

View: 394

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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.
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An Introduction to Functional Analysis in Computational Mathematics

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 ...

Author: V.I. Lebedev

Publisher: Birkhäuser

ISBN: 1461286662

Category: Mathematics

Page: 256

View: 640

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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.
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A Course in Functional Analysis and Measure Theory

Aimed at advanced undergraduate and graduate students, this book is suitable for both introductory and more advanced courses in functional analysis.

Author: Vladimir Kadets

Publisher: Springer

ISBN: 9783319920047

Category: Mathematics

Page: 539

View: 623

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Written by an expert on the topic and experienced lecturer, this textbook provides an elegant, self-contained introduction to functional analysis, including several advanced topics and applications to harmonic analysis. Starting from basic topics before proceeding to more advanced material, the book covers measure and integration theory, classical Banach and Hilbert space theory, spectral theory for bounded operators, fixed point theory, Schauder bases, the Riesz-Thorin interpolation theorem for operators, as well as topics in duality and convexity theory. Aimed at advanced undergraduate and graduate students, this book is suitable for both introductory and more advanced courses in functional analysis. Including over 1500 exercises of varying difficulty and various motivational and historical remarks, the book can be used for self-study and alongside lecture courses.
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Functional Analysis

It contains more than a thousand worked examples and exercises, which make up the main body of the book. This textbook is an introduction to functional analysis suited to final year undergraduates or beginning graduates.

Author: Joseph Muscat

Publisher: Springer

ISBN: 9783319067285

Category: Mathematics

Page: 420

View: 872

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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.
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Functional Analysis

Primarily intended for a one-semester introductory course, this text is also a perfect resource for independent study or as the basis for a reading course. This concise text provides a gentle introduction to functional analysis.

Author: Sergei Ovchinnikov

Publisher: Springer

ISBN: 9783319915128

Category: Mathematics

Page: 205

View: 634

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This concise text provides a gentle introduction to functional analysis. Chapters cover essential topics such as special spaces, normed spaces, linear functionals, and Hilbert spaces. Numerous examples and counterexamples aid in the understanding of key concepts, while exercises at the end of each chapter provide ample opportunities for practice with the material. Proofs of theorems such as the Uniform Boundedness Theorem, the Open Mapping Theorem, and the Closed Graph Theorem are worked through step-by-step, providing an accessible avenue to understanding these important results. The prerequisites for this book are linear algebra and elementary real analysis, with two introductory chapters providing an overview of material necessary for the subsequent text. Functional Analysis offers an elementary approach ideal for the upper-undergraduate or beginning graduate student. Primarily intended for a one-semester introductory course, this text is also a perfect resource for independent study or as the basis for a reading course.
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An Introduction to Functional Analysis

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 ...

Author: Charles Swartz

Publisher: CRC Press

ISBN: 0824786432

Category: Mathematics

Page: 600

View: 437

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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
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A Course in Functional Analysis

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.

Author: John B. Conway

Publisher: Springer Science & Business Media

ISBN: 0387972455

Category: Mathematics

Page: 400

View: 273

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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
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Elementary Functional Analysis

This text is an introduction to functional analysis which requires readers to have a minimal background in linear algebra and real analysis at the first-year graduate level.

Author: Charles Swartz

Publisher: World Scientific Publishing Company

ISBN: 9789813107526

Category: Science

Page: 192

View: 342

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This text is an introduction to functional analysis which requires readers to have a minimal background in linear algebra and real analysis at the first-year graduate level. Prerequisite knowledge of general topology or Lebesgue integration is not required. The book explains the principles and applications of functional analysis and explores the development of the basic properties of normed linear, inner product spaces and continuous linear operators defined in these spaces. Though Lebesgue integral is not discussed, the book offers an in-depth knowledge on the numerous applications of the abstract results of functional analysis in differential and integral equations, Banach limits, harmonic analysis, summability and numerical integration. Also covered in the book are versions of the spectral theorem for compact, symmetric operators and continuous, self adjoint operators.
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An Introduction to Functional Analysis in Computational Mathematics

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 ...

Author: V.I. Lebedev

Publisher: Springer Science & Business Media

ISBN: 0817638881

Category: Mathematics

Page: 256

View: 180

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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.
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