EMS__Several_Complex_Variables_01 .pdf

《EMS__Several_Complex_Variables_01 .pdf》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。

1、ContentsI.RemarkableFactsofComplexAnalysisA.G.Vitushkin1iII.TheMethodofIntegralRepresentationsinComplexAnalysisG.MKhenkin19m.ComplexAnalyticSetsE.M.Chirka117IV.HolomorphicMappingsandtheGeometryofHypersurfacesA.G.Vitushkin159V.GeneralTheoryofMultidimensionalResiduesP.Dolbeault215Aut

2、horIndex243■SubjectIndex246I.RemarkableFactsofComplexAnalysisA.G.VitushkinTranslatedfromtheRussianbyP.M.Gauthier

3、.ApproximationofFunctions...■8§6.IsolatingtheNon-HolomorphicPartofaFunction.10§7.ConstructionofFunctionswithGivenZeros12§8.SteinManifolds;..'..'....14§9.DeformationsofComplexStructure16Introduction?■??'"Thepresentarticlegivesashortsurveyofresultsincontemporarycomplexanalysisanditsa

4、pplications.Thematerialpresentedisconcentratedaroundseveralpivotalfactswhoseunderstandingenablesonetohaveageneralviewofthisareaofanalysis.§1.TheContinuationPhenomenonThemostimpressivefactfromcomplexanalysis-isthephenomenonofthecontinuationoffunctions(Hartogs,1906;Poincart,1907).Wee

5、lucidateits2A.G.Vitushkin!.-Isignificancetbyanexample.IfafunctionfisdefinedandholomorphicontheboundaryoraballBinw-dimensionalcomplexspaceC(n^2),thenitturnsoutthatfmay[becontinuedtoafunctionholomorphiconthewholeballB.Analogouslyiforanarbitraryboundeddomainwhosecomplementisconnected,

6、anyfunctioriholomorphicontheboundaryofsuchadomainAdmitsaholo-jmorphiccontinuationtothedomain-itself.Letusemphasizethatthisholdsonlyforn￡2.Inljtheonedimensionalcase,thisphenomenonclearly,doesnotoccur.IndeedSforeachset￡cC'andeachpointz0eC￡,thefunctionl/(z-z0)ishotomorphiconEbutcanno

7、tbeholomorphicallycontinuedtothepointz?./jThisdiscoverymarkedthebeginningofthesystematicstudyoffunctionsofseveralcomplexvariables.Twofundamentalnotions,originatinginconnectionwiththispropertyofholomorphicfunctions,are"envelopeofholomorphy"and"domain:of,holomorphy^'.LetDbeadomainora

8、compactsetinC.Theenvelopeo