応用関数解析（テキスト・第３版） Applied Functional Analysis（3 DGO）

著者名：Oden, J. Tinsley/Demkowicz, Leszek

Chapman and Hall/CRC（2017/12/01発売）

• 言語：ENG
• ISBN：9781498761147
• eISBN：9781498761154

Description

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

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