泛函分析导论-(第二版)_PDF下载[94MB-百度云]黄毅生

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本教材是学习泛函分析课程的一本入门教材，是针对中国学生编写的一本英文教材，在选材上吸收了国外的优秀本科生教材的一些精华；在编写上考虑了与中国学生所具备的基础知识衔接性，在充分地反映泛函分析中的核心内容的前提下，突出重点；在内容的处理上，体现了由浅入深，循序渐进的原则，用大量的例题对度量空间、赋范线性空间、线性算子与线性泛函、内积空间与各种算子及它们的谱分解的概念、关系、性质进行了演绎、推导与论证，

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ContentsPreface iIntroduction iiiList of Symbols viiChapter 1 Metric Spaces 11.1 Preliminaries 11.2 Definitions and Examples 61.3 Convergence of Sequences in Metric Spaces 121.4 Sets in a Metric Space 171.5 Complete Metric Spaces 251.6 Continuous Mappings on Metric Spaces 331.7 Compact Metric Spaces 381.8 Banach Fixed Point Theorem 46Chapter 2 Normed Linear Spaces. Banach Spaces 572.1 Review of Linear Spaces 572.2 Norms in Linear Spaces 592.3 Examples of Normed Linear Spaces 652.4 Finite-Dimensional Normed Linear Spaces 772.5 Linear Subspaces of Normed Linear Spaces 832.6 Quotient Spaces 902.7 Weierstrass Approximation Theorem 94Chapter 3 Inner Product Spaces. Hilbert Spaces 1013.1 Inner Products 1013.2 Orthogonality 1143.3 Orthonormal Systems 1233.4 Fourier Series 138Chapter 4 Linear Operators. Fundamental Theorems 1454.1 Bounded Linear Operators and Functionals 1454.2 Spaces of Bounded Linear Operators and Dual Spaces 1624.3 Banach-Steinhaus Theorem 1734.4 Inverses of Operators. Banach’s Theorem 1804.5 Hahn-Banach Theorem 1904.6 Strong and Weak Convergence 203Chapter 5 Linear Operators on Hilbert Spaces 2155.1 Adjoint Operators. Lax-Milgram Theorem 2155.2 Spectral Theorem for Self-adjoint Compact Operators 229Chapter 6 Differential Calculus in Normed Linear Spaces 2576.1 Gateaux and Frechet Derivatives 2576.2 Taylor’s Formula， Implicit and Inverse Function Theorems 270Bibliography 279Index 283