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美 Walter Rudin 著
店铺: 互动出版网图书专营店 出版社: 机械工业出版社 ISBN:711113415x 商品编码:1245556866 丛书名: 经典原版书库 出版时间:2003-12-01 页数:424
泛函分析(英文版 第2版) (美)Walter Rudin|15906 电子书 下载 mobi epub pdf txt
泛函分析(英文版 第2版) (美)Walter Rudin|15906-so88
泛函分析(英文版 第2版) (美)Walter Rudin|15906 pdf epub mobi txt 电子书 下载 2022
图书介绍
☆☆☆☆☆
||
美 Walter Rudin 著
店铺: 互动出版网图书专营店 出版社: 机械工业出版社 ISBN:711113415x 商品编码:1245556866 丛书名: 经典原版书库 出版时间:2003-12-01 页数:424
书[0名0]: | 泛函分析(英文版 [0第0]2版)|15906 |
图书定价: | 42元 |
图书作者: | (美)Walter Rudin |
出版社: | 机械工业出版社 |
出版日期: | 2003/12/1 0:00:00 |
ISBN号: | 711113415x |
开本: | 16开 |
页数: | 424 |
版次: | 1-1 |
内容简介 |
泛函分析是分析数[0学0]中“年轻”的分支,在各个[0领0]域均有着广泛应用。本书是泛函分析的经 典教材。作为Rudin的分析[0学0]经典著作之一,本书秉承了内容精练、结构清晰的特点。[0第0]2版新 增的内容有Kakutani不动点定理、Lamo[0no0]sov不变子空间定理以及遍历定理等。另外,还适[0当0]增 加了一些例子和习题。 |
目录 |
Preface Part I General Theory 1 Topological Vector Spaces Introduction Separation properties Linear mappings Finite-dimensional spaces Metrization Boundedness and continuity Semi[0no0]rms and local convexity Quotient spaces Examples Exercises 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 [0no0]rmed dual of a [0no0]rmed space Ad joints Compact operators Exercises 5 Some Appl_ications A continuity theorem Closed subspaces of LP-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 Transforms 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 distributions 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 Lomo[0no0]sov's invariant subspace theorem Exercises 11 Commutative Banach Algebras Ideals and homomorphisms Gelfand transforms Involutions Applications to [0no0]ncommutative 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 [0no0]rmal 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 [0No0]tes and Comments Bibliography List of Special Symbols Index |
泛函分析(英文版 第2版) (美)Walter Rudin|15906 电子书 下载 mobi epub pdf txt
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