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Other titles in the Pure and Applied Mathematics: A Wiley-Interscience Series of Texts, Monographs and Tracts series:
Applied Functional Analysis (Pure and Applied Mathematics Series)by Jean-pierre Aubin
Synopses & Reviews
A novel, practical introduction to functional analysis
In the twenty years since the first edition of Applied Functional Analysis was published, there has been an explosion in the number of books on functional analysis. Yet none of these offers the unique perspective of this new edition. Jean-Pierre Aubin updates his popular reference on functional analysis with new insights and recent discoveries-adding three new chapters on set-valued analysis and convex analysis, viability kernels and capture basins, and first-order partial differential equations. He presents, for the first time at an introductory level, the extension of differential calculus in the framework of both the theory of distributions and set-valued analysis, and discusses their application for studying boundary-value problems for elliptic and parabolic partial differential equations and for systems of first-order partial differential equations.
To keep the presentation concise and accessible, Jean-Pierre Aubin introduces functional analysis through the simple Hilbertian structure. He seamlessly blends pure mathematics with applied areas that illustrate the theory, incorporating a broad range of examples from numerical analysis, systems theory, calculus of variations, control and optimization theory, convex and nonsmooth analysis, and more. Finally, a summary of the essential theorems as well as exercises reinforcing key concepts are provided. Applied Functional Analysis, Second Edition is an excellent and timely resource for both pure and applied mathematicians.
Book News Annotation:
Aubin (University of Paris) introduces functional analysis through the simple Hilbertian structure, and blends pure mathematics with applied areas that illustrate the theory through examples from systems theory, calculus of variations, control and optimization theory, and non- smooth analysis. The second edition adds chapters on set-valued analysis and convex analysis, viability kernels and capture basins, and first-order partial differential equations.
Annotation c. Book News, Inc., Portland, OR (booknews.com)
Now in a fully revised second edition, this book offers unique, broad coverage of applications in such areas as partial differential equations, numerical analysis, convex and nonlinear analysis, and control and optimization theory. Written by a highly respected member of the numerical analysis community, this practical work combines the classic topics found in pure functional analysis with the many applied areas of the theory.
Mit diesem Buch verfolgt der Autor zwei Ziele: Erstens will er in die wichtigsten algebraischen Strukturen einführen, zweitens will er den Studenten helfen, ihre Fähigkeiten zum Arbeiten mit abstrakten Begriffen zu vervollkommnen. Die Kerngedanken werden in den ersten sechs Kapiteln vorgestellt, während der zweite Teil des Buches flexibel angelegt ist. Didaktisch sehr sinnvoll ist die beigefügte Anleitung zum Lesen, Analysieren und Aufstellen von Sätzen und Beweisen. (12/99)
Includes bibliographical references (p. 488-491) and index.
About the Author
JEAN-PIERRE AUBIN, PhD, is a professor at the Universit? Paris-Dauphine in Paris, France. A highly respected member of the applied mathematics community, Jean-Pierre Aubin is the author of sixteen mathematics books on numerical analysis, neural networks, game theory, mathematical economics, nonlinear and set-valued analysis, mutational analysis, and viability theory.
Table of Contents
The Projection Theorem.
Theorems on Extension and Separation.
Dual Spaces and Transposed Operators.
The Banach Theorem and the Banach-Steinhaus Theorem.
Construction of Hilbert Spaces.
L?2 Spaces and Convolution Operators.
Sobolev Spaces of Functions of One Variable.
Some Approximation Procedures in Spaces of Functions.
Sobolev Spaces of Functions of Several Variables and the Fourier Transform.
Introduction to Set-Valued Analysis and Convex Analysis.
Elementary Spectral Theory.
Hilbert-Schmidt Operators and Tensor Products.
Boundary Value Problems.
Differential-Operational Equations and Semigroups of Operators.
Viability Kernels and Capture Basins.
First-Order Partial Differential Equations.
Selection of Results.
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