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Beihang University

应用泛函分析

Beihang University via XuetangX

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Overview

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本课程从实变理论基础入手，学习线性空间、距离空间、赋范空间和内积空间，并进一步研究有界线性算子、对偶空间、谱、紧算子及自伴算子。

Syllabus

  • 第一章 实变理论基础
    • 1.0 引言
    • 1.1 集合与点集
    • 1.2 Lebesgue测度
    • 1.3 可测函数
    • 1.4 Lebesgue 积分
  • 第二章 空间理论
    • 2.1 线性空间
    • 2.2 距离空间
    • 2.3 赋范线性空间
    • 2.4 内积空间
    • 2.5 Banach不动点定理
  • 第三章 线性算子
    • 3.1 线性算子
    • 3.2 有界线性算子
    • 3.3 基本定理及应用
    • 3.4对偶空间与有界线性算子的共轭
    • 3.5 有界线性算子的谱
    • 3.6 紧算子
    • 3.7 自伴算子
  • 应用与拓展

    Taught by

    Wang Yongge, Xie Jiaxin, Jia Chaohua, Teng Yanmei, Lang Rongling, Liu Yang, and Lei Wang

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