[stein-shakarchi] complex analysis

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1、COMPLEXANALYSISIbookrootOctober20,2007PrincetonLecturesinAnalysisIFourierAnalysis:AnIntroductionIIComplexAnalysisIIIRealAnalysis:MeasureTheory,Integration,andHilbertSpacesPrincetonLecturesinAnalysisIICOMPLEXANALYSISEliasM.Stein&RamiShakarchiPRINCETONUNIVERSITYPRESSPRINCETONANDOXFOR

2、DCopyright©2003byPrincetonUniversityPressPublishedbyPrincetonUniversityPress,41WilliamStreet,Princeton,NewJersey08540IntheUnitedKingdom:PrincetonUniversityPress,6OxfordStreet,Woodstock,OxfordshireOX201TWAllRightsReservedLibraryofCongressControlNumber2005274996ISBN978-0-691-11385-2B

3、ritishLibraryCataloging-in-PublicationDataisavailableThepublisherwouldliketoacknowledgetheauthorsofthisvolumeforprovidingthecamera-readycopyfromwhichthisbookwasprintedPrintedonacid-freepaper.∞press.princeton.eduPrintedintheUnitedStatesofAmerica5791086TomygrandchildrenCarolyn,Alison

4、,JasonE.M.S.TomyparentsMohamed&MireilleandmybrotherKarimR.S.ForewordBeginninginthespringof2000,aseriesoffourone-semestercoursesweretaughtatPrincetonUniversitywhosepurposewastopresent,inanintegratedmanner,thecoreareasofanalysis.Theobjectivewastomakeplaintheorganicunitythatexistsbetw

5、eenthevariouspartsofthesubject,andtoillustratethewideapplicabilityofideasofanalysistootherfieldsofmathematicsandscience.Thepresentseriesofbooksisanelaborationofthelecturesthatweregiven.Whilethereareanumberofexcellenttextsdealingwithindividualpartsofwhatwecover,ourexpositionaimsatadi

6、fferentgoal:pre-sentingthevarioussub-areasofanalysisnotasseparatedisciplines,butratherashighlyinterconnected.Itisourviewthatseeingtheserelationsandtheirresultingsynergieswillmotivatethereadertoattainabetterunderstandingofthesubjectasawhole.Withthisoutcomeinmind,wehaveconcentratedont

7、hemainideasandtheoremsthathaveshapedthefield(sometimessacrificingamoresystematicapproach),andwehavebeensensitivetothehistoricalorderinwhichthelogicofthesubjectdeveloped.Wehaveorganizedourexpositionintofourvolumes,eachreflectingthematerialcoveredinasemester.Theircontentsmaybebroadlysum

8、-marizedasfollows:I.Fourie