Applied Functional Analysis

ISBN-13: 9780471179764 / Angielski / Twarda / 2000 / 520 str.

Jean Pierre Aubin

Opis

This revised edition of this text/reference contains new material for both students and researchers in pure and applied mathematics. The text covers applications over wide areas such as partial differential equations, numerical analysis, convex and nonlinear analysis, and control and optimization theory. Furthermore the author combines topics found in pure functional analysis with the applications of the abstract theory in applied areas.

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.

Recenzje

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)

Spis treści

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.

O autorze

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.

Blurb

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.