Applied Functional Analysis (eBook)

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.

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.

Exercises.

Bibliography.

Index.

"...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)