图书信息
图书目录
泛函分析及其在线性偏微分方程中的应用（影印版）
暂无简介
作者：
Alberto Bressan
定价：
135.00元
出版时间：
2022-02-25
ISBN：
978-7-04-056977-3
物料号：
56977-00
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
重点项目：
暂无
版面字数：
400.000千字
开本：
特殊
全书页数：
暂无
装帧形式：
精装
- 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
