应用泛函分析修订版(后两章)

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1、非数学类研究生用书AppliedFunctionalAnalysis应应应用用用泛泛泛函函函分分分析析析天津大学数学系编2013年11月4日目录第一章赋范线性空间上的有界线性算子
























1§1.1赋范线性空间上的有界线性算子·······························1§1.1.1有界线性算子······························································1§1.1.2线性算子的有界性和连续性·······································

2、·······3§1.1.3有界线性算子空间·························································4§1.1.4有界线性算子代数B(X)··················································6§1.2赋范线性空间上的有界线性泛函·······························6§1.2.1赋范线性空间上的有界线性泛函········································6§1.2.2对偶空间···························

3、·········································8§1.2.3有限秩算子·································································12§1.3有限维空间上的线性算子····································13§1.3.1有限维空间上的线性算子的表示········································13§1.3.2Mn×n(C)上的方阵范数···········································

4、··········15§1.3.3方阵的谱半径······························································19§1.4习题四···················································22第二章广义Fourier级数与最佳平方逼近
























25§2.1正交投影和广义Fourier级数··································25§2.1.1正交投影与正交分解······························

5、························25§2.1.2Fourier系数与Bessel不等式···············································28§2.1.3完全标准正交系及其等价条件···········································30§2.2函数的最佳平方逼近········································32§2.2.1最佳平方逼近问题·························································33§2.2.

6、2多项式逼近·································································35§2.2.3用正交多项式作函数的最佳平方逼近···································36i§2.3正交多项式···············································37§2.3.1正交多项式的基本概念和性质···········································37§2.3.2Legendre多项式·························

7、···································41§2.3.3带权函数的正交多项式···················································46§2.4曲线拟合的最小二乘法······································50§2.4.1曲线拟合的最小二乘问题·········································