Applied Functional Analysis

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John Wiley & Sons, Feb 4, 2000 - Mathematics - 495 pages
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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.
 

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Contents

A Guide to the Reader
1
Theorems on Extension and Separation
27
Dual Spaces and Transposed Operators
49
The Banach Theorem and the BanachSteinhaus Theorem
70
Construction of Hilbert Spaces
94
Some Approximation Procedures in Spaces of Functions
167
Sobolev Spaces of Functions of Several Variables and the Fourier
187
Introduction to SetValued Analysis and Convex Analysis
211
Boundary Value Problems
309
DifferentialOperational Equations and Semigroups of Operators
360
Viability Kernels and Capture Basins
385
FirstOrder Partial Differential Equations
411
Selection of Results
448
Minimax Inequalities
463
Exercises
470
Bibliography
488

Elementary Spectral Theory
259
HilbertSchmidt Operators and Tensor Products
283

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Page xi - This is quite natural, though, because each problem demands its own amount of properties that the derivative should enjoy (ie, its own degree of regularity). Without going too far by always requiring minimal assumptions, some problems could not be solved by sticking to the richest structure. The right balance between generality and readability is naturally a subjective choice.

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About the author (2000)

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.

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