[分析] complex analysis (princeton lectures in analysis, volume 2) elias m. stein, rami shakarchi

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1、COMPLEXANALYSISIbookrootOctober20,2007PrincetonLecturesinAnalysisIFourierAnalysis:AnIntroductionIIComplexAnalysisIIIRealAnalysis:MeasureTheory,Integration,andHilbertSpacesPrincetonLecturesinAnalysisIICOMPLEXANALYSISEliasM.Stein&RamiShakarchiPRINCETONUNIVERSITYPRESSPRINCETONANDOXFORDCopyright©2

2、003byPrincetonUniversityPressPublishedbyPrincetonUniversityPress,41WilliamStreet,Princeton,NewJersey08540IntheUnitedKingdom:PrincetonUniversityPress,6OxfordStreet,Woodstock,OxfordshireOX201TWAllRightsReservedLibraryofCongressControlNumber2005274996ISBN978-0-691-11385-2BritishLibraryCataloging-

3、in-PublicationDataisavailableThepublisherwouldliketoacknowledgetheauthorsofthisvolumeforprovidingthecamera-readycopyfromwhichthisbookwasprintedPrintedonacid-freepaper.∞press.princeton.eduPrintedintheUnitedStatesofAmerica5791086TomygrandchildrenCarolyn,Alison,JasonE.M.S.TomyparentsMohamed&Mirei

4、lleandmybrotherKarimR.S.ForewordBeginninginthespringof2000,aseriesoffourone-semestercoursesweretaughtatPrincetonUniversitywhosepurposewastopresent,inanintegratedmanner,thecoreareasofanalysis.Theobjectivewastomakeplaintheorganicunitythatexistsbetweenthevariouspartsofthesubject,andtoillustrateth

5、ewideapplicabilityofideasofanalysistootherfieldsofmathematicsandscience.Thepresentseriesofbooksisanelaborationofthelecturesthatweregiven.Whilethereareanumberofexcellenttextsdealingwithindividualpartsofwhatwecover,ourexpositionaimsatadifferentgoal:pre-sentingthevarioussub-areasofanalysisnotassepa

6、ratedisciplines,butratherashighlyinterconnected.Itisourviewthatseeingtheserelationsandtheirresultingsynergieswillmotivatethereadertoattainabetterunderstandingofthesubjectasawhole.Withthisoutcomeinmind,wehaveconcentratedonthemainideasandtheoremsthathaveshapedthefield(sometimessacrificingamoresyst

7、ematicapproach),andwehavebeensensitivetothehistoricalorderinwhichthelogicofthesubjectdeveloped.Wehaveorganizedourexpositionintofourvolumes,eachreflectingthematerialcoveredinasemester.Theircontentsmaybebroadlysum-marizedasfollows:I.Fourie