Elements of the Theory of Functions and Functional Analysis

基本信息

作者: A. N. Kolmogorov & S. V. Fomin

Paperback: 288页

出版社: Dover Publications (1999年2月16日)

语种: English

ISBN: 9780486406831     

产品尺寸及重量: 215 x 137 x 13 (mm)| 331g

页面参数仅供参考，具体以实物为准

书籍简介

《函数论与泛函分析初步》是世界著名数学家A.N.柯尔莫戈洛夫院士在莫斯科大学数学力学系多年讲授泛函分析教程(曾称《数学分析Ⅲ》)的基础上编写的。《函数论与泛函分析初步》是关于泛函分析与实变函数论的精细问题的严格的系统阐述，书中反映了作者的教育思想，体现了作者丰富的教学经验与方法。内容包括：集合论初步，度量空间与拓扑空间，赋范线性空间与线性拓扑空间，线性泛函与线性算子，测度、可测函数、积分，勒贝格不定积分、微分论，可和函数空间，三角函数傅里叶变换，线性积分方程，线性空间微分学概要以及附录的巴拿赫代数。

Originally published in two volumes, this advanced-level text is based on courses and lectures given by the authors at Moscow State University and the University of Moscow.

Reprinted here in one volume, the first part is devoted to metric and normal spaces. Beginning with a brief introduction to set theory and mappings, the authors offer a clear presentation of the theory of metric and complete metric spaces. The principle of contraction mappings and its applications to the proof of existence theorems in the theory of differential and integral equations receives detailed analysis, as do continuous curves in metric spaces — a topic seldom discussed in textbooks.

Part One also includes discussions of other subjects, such as elements of the theory of normed linear spaces, weak sequential convergence of elements and linear functionals, adjoint operators, and linear operator equations. Part Two focuses on an exposition of measure theory, the Lebesque interval and Hilbert Space. Both parts feature numerous exercises at the end of each section and include helpful lists of symbols, definitions, and theorems.

作者简介

A.N.柯尔莫戈洛夫，苏联数学家、教育家。1903年4月25日出生于俄罗斯坦博夫城。1939年当选为苏联科学院院士、主席团委员和数学研究所所长。1954年担任莫斯科大学数学力学系主任。1966年当选为苏联教育科学院院士。他还曾任《苏联大百科全书》数学学科的主编，长期担任《数学科学的成就》杂志的主编，创办《概率论及其应用》学术杂志和供中学生阅读的《量子》科普杂志。