Aubin Applied Functional Analysis

2. Auflage 2011
ISBN: 978-1-118-03097-4
Verlag: John Wiley & Sons
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 520 Seiten, E-Book

Reihe: Wiley Series in Pure and Applied Mathematics

A novel, practical introduction to functional analysis
In the twenty years since the first edition of Applied FunctionalAnalysis was published, there has been an explosion in the numberof books on functional analysis. Yet none of these offers theunique perspective of this new edition. Jean-Pierre Aubin updateshis popular reference on functional analysis with new insights andrecent discoveries-adding three new chapters on set-valued analysisand convex analysis, viability kernels and capture basins, andfirst-order partial differential equations. He presents, for thefirst time at an introductory level, the extension of differentialcalculus in the framework of both the theory of distributions andset-valued analysis, and discusses their application for studyingboundary-value problems for elliptic and parabolic partialdifferential equations and for systems of first-order partialdifferential equations.
To keep the presentation concise and accessible, Jean-Pierre Aubinintroduces functional analysis through the simple Hilbertianstructure. He seamlessly blends pure mathematics with applied areasthat illustrate the theory, incorporating a broad range of examplesfrom numerical analysis, systems theory, calculus of variations,control and optimization theory, convex and nonsmooth analysis, andmore. Finally, a summary of the essential theorems as well asexercises reinforcing key concepts are provided. Applied FunctionalAnalysis, Second Edition is an excellent and timely resource forboth pure and applied mathematicians.

Autoren/Hrsg.

Aubin, Jean-Pierre

Inhaltsverzeichnis

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 FourierTransform.
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 ofOperators.
Viability Kernels and Capture Basins.
First-Order Partial Differential Equations.
Selection of Results.
Exercises.
Bibliography.
Index.

Über Autor(innen)

JEAN-PIERRE AUBIN, PhD, is a professor at the UniversitéParis-Dauphine in Paris, France. A highly respected member of theapplied mathematics community, Jean-Pierre Aubin is the author ofsixteen mathematics books on numerical analysis, neural networks,game theory, mathematical economics, nonlinear and set-valuedanalysis, mutational analysis, and viability theory.