《泛函分析及其应用》读书记录目录一、第一章内容概括.........................................31.1泛函分析的发展历史与意义.............................41.2泛函分析的应用领域...................................5二、第二章函数空间.........................................62.1赋范线性空间.........................................72.1.1定义与性质.......................................82.1.2基本定理.........................................92.2内积空间.............................................92.2.1定义与性质......................................102.2.2正交性与Schwarz不等式...........................12三、第三章Hilbert空间.....................................133.1内积空间与Hilbert空间的关系.........................143.2线性算子与恒等算子..................................153.3最佳逼近理论........................................163.4希尔伯特空间中的正交分解............................17四、第四章差分方程........................................184.1差分方程的基本概念..................................194.2差分方程的解法......................................194.3C0-半群与C0-代数....................................214.4解微分方程与泛函分析的联系..........................22五、第五章拓扑学与泛函分析................................235.1拓扑空间的定义与性质................................255.2从拓扑空间到泛函分析的推广..........................265.3泛函分析在拓扑学中的应用............................27六、第六章逼近论..........................................286.1近似理论............................................296.1.1线性逼近与三角逼近..............................316.1.2非线性逼近......................................326.2核方法..............................................336.2.1支持向量机......................................346.2.2鲁棒性理论......................................366.3数学分析中的逼近理论................................376.3.1Weierstrass逼近定理.............................386.3.2Taylor公式与泰勒级数............................39七、第七章反例............................................407.1泛函分析中的反例....................................427.2数学分析中的反例....................................437.3拓扑学中的反例......................................44八、第八章结论............................................458.1泛函分析的主要成果与应用...