Librería Portfolio

Features
New sections on variational formulations and Closed Range Theorem for closed operators
Significant expansion of Closed Range Theorem in Banach spaces
Extended examinations of topology and exposition of Schwartz's spaces of test functions
Final two chapters have been heavily revised
Summary
Applied Functional Analysis, Third Edition provides a solid mathematical foundation for the subject. It motivates students to study functional analysis by providing many contemporary applications and examples drawn from mechanics and science.

This well-received textbook starts with a thorough introduction to modern mathematics before continuing with detailed coverage of linear algebra, Lebesque measure and integration theory, plus topology with metric spaces.

The final two chapters provides readers with an in-depth look at the theory of Banach and Hilbert spaces before concluding with a brief introduction to Spectral Theory.

The Third Edition is more accessible and promotes interest and motivation among students to prepare them for studying the mathematical aspects of numerical analysis and the mathematical theory of finite elements.



Table of Contents
Preliminaries

Elementary Logic and Set Theory

Relations; Functions

Cardinality of Sets

Foundations of Abstract Algebra

Elementary Topology in Rn

Elements of Differential and Integral Calculus

Linear Algebra

Vector Spaces-The Basic Concepts

Linear Transformations

Algebraic Duals; Euclidean Spaces

Lebesgue Measure and Integration

Lebesgue Measure

Lebesgue Integration Theory

Topological and Metric Spaces

Elementary Topology

Theory of Metric Spaces

Banach Spaces

Topological Vector Spaces

Hahn-Banach Extension Theorem

Bounded (Continuous) Linear Operators on Normed Spaces

Closed Operators

Topological Duals

Weak Compactness

Closed Range Theorem

Solvability of Linear Equations

Hilbert Spaces

Basic Theory

Duality in Hilbert Spaces

Elements of Spectral Theory

References