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1、EberhardFreitagRolfBusamComplexAnalysisABCProfessorDr.EberhardFreitagTranslatorDr.RolfBusamDr.DanFuleaFacultyofMathematicsFacultyofMathematicsInstituteofMathematicsInstituteofMathematicsUniversityofHeidelbergUniversityofHeidelbergImNeuenheimerFeld288ImNeuenheimerFeld2886
2、9120Heidelberg69120HeidelbergGermanyGermanyE-mail:freitag@mathi.uni-heidelberg.deE-mail:dan@mathi.uni-heidelberg.debusam@mathi.uni-heidelberg.deMathematicsSubjectClassification(2000):30-01,11-01,11F11,11F66,11M45,11N05,30B50,33E05LibraryofCongressControlNumber:2005930226I
3、SBN-103-540-25724-1SpringerBerlinHeidelbergNewYorkISBN-13978-3-540-25724-0SpringerBerlinHeidelbergNewYorkThisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,reci
4、tation,broadcasting,reproductiononmicrofilmorinanyotherway,andstorageindatabanks.DuplicationofthispublicationorpartsthereofispermittedonlyundertheprovisionsoftheGermanCopyrightLawofSeptember9,1965,initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer.Vio
5、lationsareliableforprosecutionundertheGermanCopyrightLaw.SpringerisapartofSpringerScience+BusinessMediaspringeronline.comcSpringer-VerlagBerlinHeidelberg2005PrintedinTheNetherlandsTheuseofgeneraldescriptivenames,registerednames,trademarks,etc.inthispublicationdoesnotimp
6、ly,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevantprotectivelawsandregulationsandthereforefreeforgeneraluse.Typesetting:bytheauthorsandTechBooksusingaSpringerLATEXmacropackageCoverdesign:design&productionGmbH,HeidelbergPrintedonacid-freepaperSPI
7、N:1139602440/TechBooks543210InMemoriamHansMaaß(1911–1992)PrefacetotheEnglishEditionThisbookisatranslationoftheforthcomingfourtheditionofourGermanbook“FunktionentheorieI”(Springer2005).ThetranslationandtheLATEXfileshavebeenproducedbyDanFulea.Healsomadealotofsuggestionsfori
8、mprovementwhichinfluencedtheEnglishversionofthebook.Itisapleasureforustoexpresstohimourthanks.Wealsowant
