泛函分析及其在线性偏微分方程中的应用（影印版）

样章

作者：

Alberto Bressan

定价：

135.00 元

版面字数：

400千字

开本：

特殊

装帧形式：

精装

版次：

最新版次
印刷时间：

2022年

ISBN：

978-7-04-056977-3

物料号：

56977-00

出版时间：

2022-02-25

读者对象：

学术著作

一级分类：

自然科学

二级分类：

数学与统计

三级分类：

分析

暂无

目录
- 前辅文
- 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 Fr´echet 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 H¨older 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 134
- Chapter 8. Sobolev Spaces
  - §8.1. Distributions and weak derivatives
  - §8.2. Mollifications
  - §8.3. Sobolev spaces
  - §8.4. Approximations of Sobolev functions
  - §8.5. Extension operators
  - §8.6. Embedding theorems
  - §8.7. Compact embeddings
  - §8.8. Differentiability properties
  - §8.9. Problems
- Chapter 9. Linear Partial Differential Equations
  - §9.1. Elliptic equations
  - §9.2. Parabolic equations
  - §9.3. Hyperbolic equations
  - §9.4. Problems
- Appendix. Background Material
  - §A.1. Partially ordered sets
  - §A.2. Metric and topological spaces
  - §A.3. Review of Lebesgue measure theory
  - §A.4. Integrals of functions taking values in a Banach space
  - §A.5. Mollifications
  - §A.6. Inequalities
  - §A.7. Problems
- Summary of Notation
- Bibliography
- Index