多元复分析导论

图书标准信息

• 作者 [德]谢德曼 著
• 出版社 世界图书出版公司
• 出版时间 2010-09
• 版次 1
• ISBN 9787510027277
• 定价 35.00元
• 装帧 平装
• 开本 16开
• 纸张 胶版纸
• 页数 171页

【内容简介】

TheideaforthisbookcamewhenIwasanassistantattheDepartmentofMathematicsandComputerScienceatthePhilipps-UniversityMarburg,Germany.SeveraltimesIfacedthetaskofsupportinglecturesandseminarsoncomplexanalysisofseveralvariablesandfoundoutthatthereareveryfewbooksonthesubject,comparedtothevastamountofliteratureonfunctiontheoryofonevariable,letaloneonrealvariablesorbasicalgebra.Evenfewerbooks,tomyunderstanding,werewrittenprimarilywiththestudentinmind.Soitwasquitehardtofindsupportingexamplesandexercisesthathelpedthestudenttobecomefamiliarwiththefascinatingtheoryofseveralcomplexvariables.

【目录】

preface
1elementarytheoryofseveralcomplexvariables
1.1geometryofcn
1.2holomorphicfunctionsinseveralcomplexvariables
1.2.1definitionofaholomorphicfunction
1.2.2basicpropertiesofholomorphicfunctions
1.2.3partiallyholomorphicfunctionsandthecauchy-pdemanndifferentialequations
1.3thecauchyintegralformula
1.4o（u）asatopologicalspace
1.4.1locallyconvexspaces
1.4.2thecompact-opentopologyonc（u，e）
1.4.3thetheoremsofarzela-ascoliandmontel
1.5powerseriesandtaylorseries
1.5.1summablefamiliesinbanachspaces
1.5.2powerseries
1.5.3reinhardtdomainsandlaurentexpansion

2continuationoncircularandpolycirculardomains
2.1holomorphiccontinuation
2.2representation-theoreticinterpretationofthelaurentseries
2.3hartogs'kugelsatz，specialcase

3biholomorphicmaps
3.1theinversefunctiontheoremandimplicitfunctions
3.2theriemannmappingproblem
3.3cartan'suniquenesstheorem

4analyticsets
4.1elementarypropertiesofanalyticsets
4.2theriemannremovablesingularitytheorems

5hartogs'kugelsatz
5.1holomorphicdifferentialforms
5.1.1multilinearforms
5.1.2complexdifferentialforms
5.2theinhomogenouscauchy-riemanndifferentialequations
5.3dolbeaut'slemma
5.4thekugelsatzofhartogs

6continuationontubulardomains
6.1convexhulls
6.2holomorphicallyconvexhulls
6.3bochner'stheorem

7cartan-thullentheory
7.1holomorphicallyconvexsets
7.2domainsofholomorphy
7.3thetheoremofcartan-thullen
7.4holomorphicallyconvexreinhardtdomains

8localpropertiesofholomorphicfunctions
8.1localrepresentationofaholomorphicfunction
8.1.1germofaholomorphicfunction
8.1.2thealgebrasofformalandofconvergentpowerseries
8.2theweierstrasstheorems
8.2.1theweierstrassdivisionformula
8.2.2theweierstrasspreparationtheorem
8.3algebraicpropertiesofc{z1，.，zn}
8.4hilbert'snullstellensatz
8.4.1germsofaset
8.4.2theradicalofanideal
8.4.3hilbert'snullstellensatzforprincipalidealsregisterofsymbols
bibliography
index