[Raghavan_Narasimhan]Several Complex Variables

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1、ChicagoLecturesinMathematicsseveralcomplexvariablesRaghavanNarasimhanTheUniversityofChicagoPressChicagoandLondonChicagoLecturesinMathematicsSeriesIrvingKaplansky,EditorTheTheoryofSheaves,byRichardG.Swan(1964)TopicsinRingTheory,byI.N.Herstein(1969)FieldsandRings,byIrvingKaplansky(1969)Infinite

2、AbelianGroupTheory,byPhillipA.Griffith(1970)TopicsinOperatorTheory,byRichardBeals(1971)LieAlgebrasandLocallyCompactGroups,byIrvingKaplansky(1971)SeveralComplexVariables,byRaghavanNarasimhan(1971)InternationalStandardBookNumber:Cloth,0-226-56816-4.Paper,0-226-56817-2LibraryofCongressCatalogCar

3、dNumber:75-166949TheUniversityofChicagoPress,Chicago60637TheUniversityofChicagoPress,Ltd.,London©1971bytheUniversityofChicagoAllrightsreservedPublished1971PrintedintheUnitedStatesofAmericaCONTENTSPREFACEixGHAPTER1.ELEMENTARYPROPERTIESOFFUNCTIONSOFSEVERALCOMPLEXVARIABLESiNotations.Holomorphicf

4、unctions.Cauchy'sformulaandsomeconsequences.Theopenmappingtheorem.Weierstrass'andMontel'stheorems.CHAPTER2.ANALYTICCONTINUATION:ELEMENTARYTHEORY12Extensionofholomorphicfunctions,fromtheboundaryofapolydisc.Reinhardtdomains.CHAPTER3.SUBHARMONICFUNCTION'SANDHARTOGS'THEOREM30Definitionandbasicpro

5、pertiesofhl'rmonicandsubharmonicfunctions.Someexamplesandapp~cations.Hartogs'theoremonseparateanalyticity.Exceptionalsetsofsubharmonicfunctions.CHAPTER4.HARTOGS'THEOREMONTHESINGULARITIESOFHOLOMORPHICFUNCTIONS50Analyticsets.TheRiemanncontinuationtheorem.Rado'stheorem.Hartogs'continuitytheorem.

6、PropertiesoftheHartogsradius.AnalyticityofcertainSingularsets.vviCHAPTER5.AUTOMORPHISMSOFBOUNDEDDOMAINS65Cartan'suniquenesstheorem.Automorphismsofcirculardomains,inparticularofpolydiscs.Poincare'stheoremthatthepolydiscandtheballareanalyticallydistinct.Properholo-morphicmaps.AtheoremofRemmert-

7、SteinandSomegeneralizations.Limitsofautomorphisms:Cartan'stheorem.ActionofAut(D}onD,finitegenerationofsomediscretegroups.AninjectiveholomorphicmapfromDC