泛函分析

出版时间：1999-6  出版社：世界图书出版公司  作者：K.Yosida著  页数：500  
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内容概要

he present book is based on lectures given by the author at the University of Tokyo during the past ten years. It is intended as a textbook to be studied by students on their own or to be used in a course on Functional Analysis, i.e., the general theory of linear operators infunction spaces together with salient features of its application to diverse fields of modem and classical analysis. Necessary prerequisites for the reading of this book are summarized,with or without proof, in Chapter 0 under titles: Set Theory, Topological Spaces, Measure Spaces and Linear Spaces. Then, starting with the chapter on Semi-norms, a general theory of Banach and Hilbert spaces is presented in connection with the theory of generalized functions of S. L. SOBOLEV and L. SCHWARTZ. While the book is primarily addressed to graduate students, it is hoped it might prove useful to research mathematicians, both pure and applied. The reader may pass, e.g., fromChapter IX (Analytical Theory. of Semi-groups) directly to Chapter XIII (Ergodic Theory and Diffusion Theory) and to Chapter XIV (Integration of the Equation of Evolution). Such materials as "Weak Topologies and Duality in Locally Convex Spaces" and "Nuclear Spaces" are presented in the form of the appendices to Chapter V and Chapter X,respectively. These might be skipped for the first reading by those who are interested rather in the application of linear operators.

书籍目录

Contents　0. Preliminaries　1. Set Theory　2. Topological Spaces　3. Measure Spaces　4. Linear SpacesI. Semi-nonns　1. Semi-nonns and Locally Convex Linear Topological Spaces　2. Nonns and Quasi-nonns　3. Examples of Normed Linear Spaces　4. Examples of Quasi-nonned Linear Spaces　5. Pre-Hilbert Spaces　6. Continuity of Linear Operators　7. Bounded Sets and Bomologic Spaces　8. Generalized Functions and Generalized Derivatives　9. B-spaces and F-spaces　10. Tbe Completion　11. Factor Spaces of a B-space　12. The Partition of Unity　13. Generalized Functions with Compact Support　14. The Direct Product of Generalized FunctionsII. Applications of the Baire-Hausdorff Theorem　1. The Unifonn Boundedness Theorem and the Resonance Theorem　2. The Vitali-Hahn-Saks Theorem　3. The Termwise Differentiability of a Sequence of Generalized Functions　4. The Principle ot the Condensation of Singularities　5. The Open Mapping Theorem　6. The Closed Graph Theorem　7. An Application of the Closed Graph Theorem (Hormander's Theorem)III. The Orthogonal Projection and F. Riesz Representation Theo-rem　1. The Orthogonal Projection　2. "Nearly Orthogonal" Elements　……IV. The Hahn-Banach TheoremsV. Strong Convergence and Weak ConvergenceVI. Fourier Transform and Differential EquationsVII. Dual OperatorsVIII. Resolvent and SpectrumIX. Analytical Theory of Semi-groupsX Compact OperatorsXI. Nonned Rings and Spectral RepresentationXII. Other Representation Theorems in Linear SpacesXIIT. Ergodic Theory and Diffusion TheoryXIV The Integration of the Equation of EvolutionSupplementary NotesBibliographyIndexNotation of Spaces

用户评论 (总计14条)

•   吉田耕作大人的大作，全书像本字典，颇有rudin的风范。
•   日本人的书，不少还是很有水准的
•   大师写的书就是好流畅如行云流水我导师看了7遍可他说有个长江学者把这本书背下来了
•   介绍翔实，不愧为经典之作
•   降价买滴，价廉物美，就是东西送到滴时候书角是皱滴
•   过于专业了，如果不是做泛函方向，没有必要看这么有深度的书，鲁丁的那本泛函就够了。
•   还可以吧，就是有些纸张透明使反面的字也映到正面上来了，看起来很不舒服。有一少部分公式的上标下标也看不清楚。
•   这本书是经典泛函分析中最全面的介绍，许多其他书中没有的东西都可以在这里找到清晰的解答。本书的例子非常丰富，是一本非常好的书，尤其是泛函分析专业的重要参考文献。
•   经典专业书，但遗憾的是该版2012年版，字体稍小，排版有些密，公式显得更挤，看着很不舒服！纸张也薄，世图的书有些好，但这版书价格高，印刷没有邮电的ross影印的好！冲着内容给五颗星！
•   很适合当泛函分析的辞典使用。如果有时间能够读完的话，那么就是泛函小牛
•   希望货配齐之后再发货！
•   吉田耕作（东大毕业）乃泛函分析领域的大牛，书写得很到位，要啃下来还是不容易的一件事
•   挺好的，经典专业基础书，值得拥有！
•   字典一本，很多泛函书上找不到的定理证明都能在这里找到