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1、SeveralComplexVariablesandIntegralFormulasSeveralComplexSeveralComplexVariablesandVariablesandIntegralFormulasIntegralFormulasKenzoAdachiNagasakiUniversity,JapanWorldScienti?cNEWJERSEY?LONDON?SINGAPORE?BEIJING?SHANGHAI?HONGKONG?TAIPEI?CHENNAIPublishedbyWorldScientificPublishingCo.Pte.Ltd.5TohTuckLi
2、nk,Singapore596224USAoffice:27WarrenStreet,Suite401-402,Hackensack,NJ07601UKoffice:57SheltonStreet,CoventGarden,LondonWC2H9HEBritishLibraryCataloguing-in-PublicationDataAcataloguerecordforthisbookisavailablefromtheBritishLibrary.SEVERALCOMPLEXVARIABLESANDINTEGRALFORMULASCopyright?2007byWorldScienti
3、ficPublishingCo.Pte.Ltd.Allrightsreserved.Thisbook,orpartsthereof,maynotbereproducedinanyformorbyanymeans,electronicormechanical,includingphotocopying,recordingoranyinformationstorageandretrievalsystemnowknownortobeinvented,withoutwrittenpermissionfromthePublisher.Forphotocopyingofmaterialinthisvol
4、ume,pleasepayacopyingfeethroughtheCopyrightClearanceCenter,Inc.,222RosewoodDrive,Danvers,MA01923,USA.Inthiscasepermissiontophotocopyisnotrequiredfromthepublisher.ISBN-13978-981-270-574-7ISBN-10981-270-574-0PrintedinSingapore.LaiFun-SeveralComplex.pmd112/4/2006,11:06AMDecember19,200618:26WSPC/BookTr
5、imSizefor9inx6inws-book9x6TomyfamilyMachiko,HidehikoandYukovDecember19,200618:26WSPC/BookTrimSizefor9inx6inws-book9x6PrefaceTheaimofthisbookistostudysomeimportantresultsobtainedinthelast50yearsinthefunctiontheoryofseveralcomplexvariablesthataremainlyconcernedwiththeextensionofholomorphicfunctionsfr
6、omsubmanifoldsofpseudoconvexdomainsandestimatesforsolutionsofthe?ˉprobleminpseudoconvexdomains.Thisbookisdividedinto?vechapters.InChapter1werecalltheelementarytheoryoffunctionsofseveralcomplexvariables.Weprovethateverydomainofholomorphyisapseudo-convexopenset.Moreover,wegivetheproofoftheHartogstheo
7、remwhichmeansthataseparatelyanalyticfunctionisanalytic.InChapter2wedealwithL2estimatesforthe?ˉprobleminpseudo-nconvexdomainsinCduetoH¨ormander.Asanapplication,wegivethea?rmativeanswerfortheLeviproblem.Moreo
