Applied Functional Analysis

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Jean-Pierre Aubin updates his popular reference on functional analysis with new insights and recent discoveriesadding 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 ...
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Overview

Jean-Pierre Aubin updates his popular reference on functional analysis with new insights and recent discoveriesadding 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.
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Editorial Reviews

Booknews
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)
From the Publisher
“…full of interesting and/or amazing comments…an original and valuable contribution to functional analysis…” (Bulletin of The Belgian Mathematical Society, Vol.11, No.4, 2004)

"Reflects author's background in numerical analysis, partial differential equations, and mathematical economics.... Good exercises." (American Mathematical Monthly, November 2001)

"The second edition has made some additions and some deletions..." (Zentralblatt MATH, Vol. 946, No. 21)

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Product Details

Meet the Author

JEAN-PIERRE AUBIN, PhD, is a professor at the Université 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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Table of Contents

Preface
Introduction: A Guide to the Reader 1
1 The Projection Theorem 4
2 Theorems on Extension and Separation 27
3 Dual Spaces and Transposed Operators 49
4 The Banach and the Banach-Steinhaus Theorem 70
5 Construction of Hilbert Spaces 94
6 L[superscript 2] Spaces and Convolution Operators 120
7 Sobolev Spaces of Functions of One Variable 145
8 Some Approximation Procedures in Spaces of Functions 167
9 Sobolev Spaces of Functions of Several Variables and the Fourier Transform 187
10 Introduction to Set-Valued Analysis and Convex Analysis 211
11 Elementary Spectral Theory 259
12 Hilbert-Schmidt Operators and Tensor Products 283
13 Boundary Value Problems 309
14 Differential-Operational Equations and Semigroups of Operators 360
15 Viability Kernels and Capture Basins 385
16 First-Order Partial Differential Equations 411
Selection of Results 448
Exercises 470
Bibliography 488
Index 493
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