Introductory Functional Analysis with Applications

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Author: Kreyszig

Publisher: John Wiley & Sons

ISBN: 9788126511914

Category: Functional analysis

Page: 704

View: 7507

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

Introductory Functional Analysis

With Applications to Boundary Value Problems and Finite Elements

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Author: B.D. Reddy

Publisher: Springer Science & Business Media

ISBN: 1461205751

Category: Mathematics

Page: 472

View: 2191

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.

Partielle Differentialgleichungen

Eine Einführung

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Author: Walter A. Strauss

Publisher: Springer-Verlag

ISBN: 366312486X

Category: Mathematics

Page: 458

View: 7882

Dieses Buch ist eine umfassende Einführung in die klassischen Lösungsmethoden partieller Differentialgleichungen. Es wendet sich an Leser mit Kenntnissen aus einem viersemestrigen Grundstudium der Mathematik (und Physik) und legt seinen Schwerpunkt auf die explizite Darstellung der Lösungen. Es ist deshalb besonders auch für Anwender (Physiker, Ingenieure) sowie für Nichtspezialisten, die die Methoden der mathematischen Physik kennenlernen wollen, interessant. Durch die große Anzahl von Beispielen und Übungsaufgaben eignet es sich gut zum Gebrauch neben Vorlesungen sowie zum Selbststudium.

Functional Analysis, Sobolev Spaces and Partial Differential Equations

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Author: Haim Brezis

Publisher: Springer Science & Business Media

ISBN: 0387709134

Category: Mathematics

Page: 600

View: 2416

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.

Applied Functional Analysis

Numerical Methods, Wavelet Methods, and Image Processing

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Author: Abul Hasan Siddiqi

Publisher: CRC Press

ISBN: 9780203913017

Category: Mathematics

Page: 660

View: 8500

The methods of functional analysis have helped solve diverse real-world problems in optimization, modeling, analysis, numerical approximation, and computer simulation. Applied Functional Analysis presents functional analysis results surfacing repeatedly in scientific and technological applications and presides over the most current analytical and numerical methods in infinite-dimensional spaces. This reference highlights critical studies in projection theorem, Riesz representation theorem, and properties of operators in Hilbert space and covers special classes of optimization problems. Supported by 2200 display equations, this guide incorporates hundreds of up-to-date citations.

Einführung in die Funktionalanalysis

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Author: Reinhold Meise,Dietmar Vogt

Publisher: Springer-Verlag

ISBN: 3322803104

Category: Mathematics

Page: 416

View: 3964

Dieses Buch wendet sich an Studenten der Mathematik und der Physik, welche über Grundkenntnisse in Analysis und linearer Algebra verfügen.

Applications of Functional Analysis and Operator Theory

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Author: V. Hutson,J. Pym,M. Cloud

Publisher: Elsevier

ISBN: 9780080527314

Category: Mathematics

Page: 432

View: 7504

Functional analysis is a powerful tool when applied to mathematical problems arising from physical situations. The present book provides, by careful selection of material, a collection of concepts and techniques essential for the modern practitioner. Emphasis is placed on the solution of equations (including nonlinear and partial differential equations). The assumed background is limited to elementary real variable theory and finite-dimensional vector spaces. Key Features - Provides an ideal transition between introductory math courses and advanced graduate study in applied mathematics, the physical sciences, or engineering. - Gives the reader a keen understanding of applied functional analysis, building progressively from simple background material to the deepest and most significant results. - Introduces each new topic with a clear, concise explanation. - Includes numerous examples linking fundamental principles with applications. - Solidifies the reader’s understanding with numerous end-of-chapter problems. · Provides an ideal transition between introductory math courses and advanced graduate study in applied mathematics, the physical sciences, or engineering. · Gives the reader a keen understanding of applied functional analysis, building progressively from simple background material to the deepest and most significant results. · Introduces each new topic with a clear, concise explanation. · Includes numerous examples linking fundamental principles with applications. · Solidifies the reader's understanding with numerous end-of-chapter problems.

Linear Functional Analysis

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Author: Bryan P. Rynne,Martin A. Youngson

Publisher: Springer Science & Business Media

ISBN: 9781852332570

Category: Mathematics

Page: 273

View: 8024

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.

Funktionalanalysis

Theorie und Anwendung

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Author: Harro Heuser

Publisher: Vieweg+teubner Verlag

ISBN: 9783835100268

Category: Mathematics

Page: 696

View: 1203

Das vorliegende Buch vermittelt nicht nur die Grundbegriffe, Haupttheoreme und tragenden Methoden der Funktionalanalysis in lebendiger und eingangiger Weise, sondern entwickelt dies aus den praktischen Fragestellungen der Naturwissenschaften und der klassischen Analysis. Eine Vielzahl von Beispielen und Aufgaben hilft bei der Vertiefung und Einubung des Gelernten.

From Vector Spaces to Function Spaces

Introduction to Functional Analysis with Applications

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Author: Yutaka Yamamoto

Publisher: SIAM

ISBN: 9781611972313

Category: Engineering mathematics

Page: 268

View: 9403

This book provides a treatment of analytical methods of applied mathematics. It starts with a review of the basics of vector spaces and brings the reader to an advanced discussion of applied mathematics, including the latest applications to systems and control theory. The text is designed to be accessible to those not familiar with the material and useful to working scientists, engineers, and mathematics students. The author provides the motivations of definitions and the ideas underlying proofs but does not sacrifice mathematical rigor. From Vector Spaces to Function Spaces presents: an easily accessible discussion of analytical methods of applied mathematics from vector spaces to distributions, Fourier analysis, and Hardy spaces with applications to system theory; an introduction to modern functional analytic methods to better familiarize readers with basic methods and mathematical thinking; and an understandable yet penetrating treatment of such modern methods and topics as function spaces and distributions, Fourier and Laplace analyses, and Hardy spaces.

Reelle und Komplexe Analysis

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Author: Walter Rudin

Publisher: Walter de Gruyter

ISBN: 9783486591866

Category: Analysis - Lehrbuch

Page: 499

View: 6584

Besonderen Wert legt Rudin darauf, dem Leser die Zusammenhänge unterschiedlicher Bereiche der Analysis zu vermitteln und so die Grundlage für ein umfassenderes Verständnis zu schaffen. Das Werk zeichnet sich durch seine wissenschaftliche Prägnanz und Genauigkeit aus und hat damit die Entwicklung der modernen Analysis in nachhaltiger Art und Weise beeinflusst. Der "Baby-Rudin" gehört weltweit zu den beliebtesten Lehrbüchern der Analysis und ist in 13 Sprachen übersetzt. 1993 wurde es mit dem renommierten Steele Prize for Mathematical Exposition der American Mathematical Society ausgezeichnet. Übersetzt von Uwe Krieg.

Introduction to Hilbert Spaces with Applications

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Author: Lokenath Debnath,Piotr Mikusiński

Publisher: N.A

ISBN: 9780122084362

Category: Mathematics

Page: 551

View: 1335

Continuing on the success of the previous edition, Introduction to Hilbert Spaces with Applications, Second Edition , offers an overview of the basic ideas and results of Hilbert space theory and functional analysis. It acquaints students with the Lebesque integral, and includes an enhanced presentation of results and proofs. Students and researchers benefit from the wealth of revised examples in new, diverse applications as they apply to optimization, variational and control problems, and problems in approximation theory, nonlinear instability, and bifurcation. The text also includes a new, well-researched chapter on wavelets. Students and researchers agree that this is the definitive text on Hilbert Space theory.

Maß und Integral

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Author: Martin Brokate,Götz Kersting

Publisher: Springer-Verlag

ISBN: 303460646X

Category: Mathematics

Page: 160

View: 7017

Der Integralbegriff in seiner Ausprägung durch Henri Lebesgue ist ein grundlegendes Werkzeug in der modernen Analysis, Numerik und Stochastik. Für Lehrveranstaltungen zu diesen Gebieten der Mathematik bereiten die Autoren wesentliche Sachverhalte in kompakter Weise auf. Das Buch liefert Orientierung und Material für verschiedene Varianten zwei- oder vierstündiger Lehrveranstaltungen. In einem ergänzenden Abschnitt werden um den Begriff der Konvexität herum Verbünde zur Funktionalanalysis hergestellt.

Measure, Integral, Derivative

A Course on Lebesgue's Theory

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Author: Sergei Ovchinnikov

Publisher: Springer Science & Business Media

ISBN: 1461471966

Category: Mathematics

Page: 146

View: 8072

This classroom-tested text is intended for a one-semester course in Lebesgue’s theory. With over 180 exercises, the text takes an elementary approach, making it easily accessible to both upper-undergraduate- and lower-graduate-level students. The three main topics presented are measure, integration, and differentiation, and the only prerequisite is a course in elementary real analysis. In order to keep the book self-contained, an introductory chapter is included with the intent to fill the gap between what the student may have learned before and what is required to fully understand the consequent text. Proofs of difficult results, such as the differentiability property of functions of bounded variations, are dissected into small steps in order to be accessible to students. With the exception of a few simple statements, all results are proven in the text. The presentation is elementary, where σ-algebras are not used in the text on measure theory and Dini’s derivatives are not used in the chapter on differentiation. However, all the main results of Lebesgue’s theory are found in the book. http://online.sfsu.edu/sergei/MID.htm

An Introduction to Functional Analysis

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Author: Charles Swartz

Publisher: CRC Press

ISBN: 9780824786434

Category: Mathematics

Page: 600

View: 3663

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

Lineare Funktionalanalysis

Eine anwendungsorientierte Einführung

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Author: Hans Wilhelm Alt

Publisher: Springer-Verlag

ISBN: 3662083868

Category: Mathematics

Page: 294

View: 6333

Linear Functional Analysis

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Author: Joan Cerda

Publisher: American Mathematical Soc.

ISBN: 0821851152

Category: Mathematics

Page: 330

View: 2682

"Functional analysis studies the algebraic, geometric, and topological structures of spaces and operators that underlie many classical problems. Individual functions satisfying specific equations are replaced by classes of functions and transforms that are determined by the particular problems at hand. This book presents the basic facts of linear functional analysis as related to fundamental aspects of mathematical analysis and their applications. The exposition avoids unnecessary terminology and generality and focuses on showing how the knowledge of these structures clarifies what is essential in analytic problems. The material in the first part of the book can be used for an introductory course on functional analysis, with an emphasis on the role of duality. The second part introduces distributions and Sobolev spaces and their applications. Convolution and the Fourier transform are shown to be useful tools for the study of partial differential equations. Fundamental solutions and Green's functions are considered and the theory is illustrated with several applications. In the last chapters, the Gelfand transform for Banach algebras is used to present the spectral theory of bounded and unbounded operators, which is then used in an introduction to the basic axioms of quantum mechanics. The presentation is intended to be accessible to readers whose backgrounds include basic linear algebra, integration theory, and general topology. Almost 240 exercises will help the reader in better understanding the concepts employed."--Publisher's description.