Applied Functional Analysis

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John Wiley & Sons, Sep 30, 2011 - Mathematics - 520 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

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 Theorem and the BanachSteinhaus Theorem
70
5 Construction of Hilbert Spaces
94
6 L2 Spaces and Convolution Operators
120
7 Sobolev Spaces of Functions of One Variable
145
11 Elementary Spectral Theory
259
12 HilbertSchmidt Operators and Tensor Products
283
13 Boundary Value Problems
309
14 DifferentialOperational Equations and Semigroups of Operators
360
15 Viability Kernels and Capture Basins
385
16 FirstOrder Partial Differential Equations
411
Selection of Results
448
Exercises
470

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 SetValued Analysis and Convex Analysis
211

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About the author (2011)

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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