泛函分析（英文版·原书第2版·典藏版）
| 作者 |
| [美]沃尔特·鲁丁（Walter Rudin） |
| 丛书名 |
| 华章数学原版精品系列 |
| 出版社 |
| 机械工业出版社 |
| ISBN |
| 9787111654742 |
| 简要 |
| 简介 |
| 内容简介书籍数学书籍 本书不仅详细叙述了拓扑线性空间，包括若干子类局部凸空间、赋范空间、内积空间的公理系统、结构属性及其之上的强弱拓扑、共轭性，还深入论述了该学科离不开的几个专题，即形式上更为一般的三大基本定理与泛函延拓定理, Banach代数特别是Gelfand变换的基本理论，紧算子及其谱理论，自伴算子的谱理论，无界正常算子的谱理论以及Bonsall的闭值域定理，不变子空间的Lomonosov定理等；而且给出了以上基本理论的丰富多彩的应用，包括完整的关于广义函数、Fourier变换及其偏微分方程基本解的论述，对于Tauber型定理的应用，von Neumann的平均遍历定理，算子半群的Hille-Yosida定理并应用于发展方程等。 |
| 目录 |
| Preface About thd Author Part I General Theory Topological Vector Spaces Introduction Separation properties Linear mappings Finite-dimensional spaces Metrization Boundedness and continuity Seminorms and local convexity Quotient spaces Examples Exercises 2 Completeness Baire category The Banach-Steinhaus theorem The open mapping theorem The closed graph theorem Bilinear mappings Exercises 3 Convexity The Hahn-Banach theorems Weak topologies Compact convex sets Vector-valued integration Holomorphic functions Exercises 4 Duality in Banach Spaces The normed dual of a normed space Adjoints Compact operators Exercises 5 Some Applications A continuity theorem Closed subspaces of fi-spaces The range of a vector-valued measure A generalized Stone-Weierstrass theorem Two interpolation theorems Kakutani's fixed point theorem Haar measure on compact groups Uncomplemented subspaces Sums of Poisson kernels Two more fixed point theorems Exercises Part II Distributions and Fourier Transform 6 Test Functions and Distributions Introduction Test function spaces Calculus with distributions Localization Supports of distributions Distributions as derivatives Convolutions Exercises 7 Fourier Transforms Basic properties Tempered d]str]but]ons Paley-Wiener theorems Sobolev's lemma Exercises 8 Applications to Differential Equations Fundamental solutions Elliptic equations Exercises 9 Tauberian Theory Wiener's theorem The prime number theorem The renewal equation Exercises Part III Banach Algebras and Spectral Theory 10 Banach Algebras Introduction Complex homomorphisms Basic properties of spectra Symbolic calculus The group of invertible elements Lomonosov's invariant subspace theorem Exercises 11 Commutative Banach Algebras Ideals and homomorphisms Gelfand transforms Involutions Applications to noncommutative algebras Positive functionals Exercises 12 Bounded Operators on a Hilbert Space Basic facts Bounded operators A commutativity theorem Resolutions of the identity The spectral theorem Eigenvalues of normal operators Positive operators and square roots The group of invertible operators A characterization of B*-algebras An ergodic theorem Exercises 13 Unbounded Operators Introduction Graphs and symmetric operators The Cayley transform Resolutions of the identity The spectral theorem Semigroups of operators Exercises Appendix A Compactness and Continuity Appendix B Notes and Comments Bibliography List of Special Symbols Index |
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