泛函分析及其在线性偏微分方程中的应用（影印版）

本书以简洁的方式介绍 了泛函分析的所有基本概念 和结果，略去了更专的主题 。作者根据需要介绍了足够 的Sobolev空间和线性算子 半群的理论，用以发展泛函 分析在椭圆型、抛物型和双 曲型偏微分方程中的重要应 用。贯穿全书，作者详尽解 释了泛函分析中的定理与有 限维线性代数中的熟知结果 之间的联系。 本书使用了大量插图来 解释证明中用到的主要概念 和思想，大部分章节末尾都 包含了数量可观的习题。 本书可作为一学期研究 生课程的教材，也可供对泛 函分析和偏微分方程感兴趣 的相关专业的研究生阅读参 考。

Preface Chapter 1.Introduction §1.1.Linear equations §1.2.Evolution equations §1.3.Function spaces §1.4.Compactness Chapter 2.Banach Spaces §2.1.Basic definitions §2.2.Linear operators §2.3.Finite-dimensional spaces §2.4.Seminorms and Fréchet spaces §2.5.Extension theorems §2.6.Separation of convex sets §2.7.Dual spaces and weak convergence §2.8.Problems Chapter 3.Spaces of Continuous Functions §3.1.Bounded continuous functions §3.2.The Stone-Weierstrass approximation theorem §3.3.Ascoli's compactness theorem §3.4.Spaces of Holder continuous functions §3.5.Problems Chapter 4.Bounded Linear Operators §4.1.The uniform boundedness principle §4.2.The open mapping theorem §4.3.The closed graph theorem §4.4.Adjoint operators §4.5.Compact operators §4.6.Problems Chapter 5.Hilbert Spaces §5.1.Spaces with an inner product §5.2.Orthogonal projections §5.3.Linear functionals on a Hilbert space §5.4.Gram-Schmidt orthogonalization §5.5.Orthonormal sets §5.6.Positive definite operators §5.7.Weak convergence §5.8.Problems Chapter 6.Compact Operators on a Hilbert Space §6.1.Fredholm theory §6.2.Spectrum of a compact operator §6.3.Selfadjoint operators §6.4.Problems Chapter 7.Semigroups of Linear Operators §7.1.Ordinary differential equations in a Banach space §7.2.Semigroups of linear operators §7.3.Resolvents §7.4.Generation of a semigroup §7.5.Problems Chapter 8.Sobolev Spaces §8.1.Distributions and weak derivatives