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实解析函数入门-第2版-(影印版)

作者：（美）克兰兹　著

出版社：世界图书出版公司

出版年：2013-03-01

评分：5分

ISBN：9787510058134

所属分类：教辅教材

书刊介绍

实解析函数入门-第2版-(影印版) 内容简介

the subject of real analytic functions is one of the oldest inmathematical analysis. today it is encountered early in one'smathematical training： the first taste usually comes rn calculus.while most working mathematicians use real analytic functions fromtime to time in their wofk， the vast lore of real analyticfunctions remains obscure and buried in the literature. it isremarkable that the most accessible treatment of puiseux's thcoremis in lefschetz's quute old algebraic geometry， that the clearestdiscussion of resolution of singularities for real analyticmanifolds is in a book review by michael atiyah， that there is nocompre hensive discussion in print of the embedding problem forreal analytic manifolds.we have had occasion in our collaborative research to becomeacquainted with both the history and the scope of the theory ofreal analytic functions. it seems both appropriate and timely forus to gather together this information in a single volume. thematerial presented here is of three kinds. the elementary topics，covered in chapter 1， are presented in great detail. even resultslike a real analytic inverse function theorem are difficult to findin the literature， and we take pains here to present such topicscarefully. topics of middling difficulty， such as separate realanalyticity， puiseux series， the fbi transform， and related ideas（chapters 2-4）， are covered thoroughly but rather morebriskly. finally there are some truly deep and difficult topics：embedding of real analytic manifolds， sub and semi-analytic sets，the structure theorem for real analytic varieties， and resolutionof singularities are disc，ussed and described. but thorough proofsin these areas could not possibly be provided in a volume of modestlength.

实解析函数入门-第2版-(影印版) 本书特色

《实解析函数入门(第2版)》编著者克兰兹。The subject of real analytic functions is one of the oldest in mathematical analysis. Today it is encountered early in one's mathematical training： the first taste usually comes rn calculus. While most working mathematicians use real analytic functions from time to time in their WOfk， the vast lore of real analytic functions remains obscure and buried in the literature. It is remarkable that the most accessible treatment of Puiseux's thcorem is in Lefschetz's quute old Algebraic Geometry， that the clearest discussion of resolution of singularities for real analytic manifolds is in a book review by Michael Atiyah， that there is no compre hensive discussion in print of the embedding problem for real analytic manifolds.

实解析函数入门-第2版-(影印版) 目录

prethce to the second edition
preface to the first edition
1 elementary propertles
1.1 basic properties of power series
1.2 analytic continuation
1.3 the formula of faa di bruno
1.4 composition of reai analytic functions
1.5 inverse functions .
2 multivariable calculus of reai analytic functions
2.1 power series in several variables
2.2 reai analytic functions of severai variables
2.3 thelmplicit function theorem
2.4a special case of the cauchy-kowalewsky theorem
2.5 the lnverse function theorem
2.6topologies on the space of real analytic functions
2.7 reai analytic submarufolds
2.7.1bundles over a real analytic submanifold
2.8 the generai cauchy-kowalewsky theorem
3 classicai toplcs
3.0 introductory remarks
3.1 thetheorem ofpringsheim and boas
3.2 besicovitch'stheorem
3.3 whitney's extension and approximation theorems
3.4 thetheorem ofs.bernstein
4some questions of hard analysis
4.1 quasi-analytic and gevrey classes
4.2 puiseuxseries
4.3 separate real analyticity
5 results motivated by partial differentiai equations
5.1 division of distributionsl
5.1.1projection of polynomially defined sets
5.2 dmsion of distributionsll
5.3 the fbi transform
5.4 the paley-wiener theorem
6 topics in geometry
6.1 the weierstrass preparation theorem
6.2 resolution of singularities
6.3 lojasiewicz's structure theorem for real analyticvarieties
6.4 the embedding of real analytic manifolds
6.5 semianalytic and subanalytic sets
6.5.1 basic definitions
6.5.2 facts concerning semianalytic and subanalytic sets
6.5.3 examples and discussion
6.5.4 rectilinearization
blbliography
index