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1、IbookrootOctober20,2007FOURIERANALYSISIbookrootOctober20,2007PrincetonLecturesinAnalysisIFourierAnalysis:AnIntroductionIIComplexAnalysisIIIRealAnalysis:MeasureTheory,Integration,andHilbertSpacesIbookrootOctober20,2007PrincetonLecturesinAnalysisIFOURIERANALYSISanintroductionEliasM.Stein&RamiShakarch
2、iPRINCETONUNIVERSITYPRESSPRINCETONANDOXFORDCopyright©2003byPrincetonUniversityPressPublishedbyPrincetonUniversityPress,41WilliamStreet,Princeton,NewJersey08540IntheUnitedKingdom:PrincetonUniversityPress,6OxfordStreet,Woodstock,OxfordshireOX201TWAllRightsReservedLibraryofCongressControlNumber2003103
3、688ISBN978-0-691-11384-5BritishLibraryCataloging-in-PublicationDataisavailableThepublisherwouldliketoacknowledgetheauthorsofthisvolumeforprovidingthecamera-readycopyfromwhichthisbookwasprintedPrintedonacid-freepaper.∞press.princeton.eduPrintedintheUnitedStatesofAmerica5791086IbookrootOctober20,2007
4、TomygrandchildrenCarolyn,Alison,JasonE.M.S.TomyparentsMohamed&MireilleandmybrotherKarimR.S.IbookrootOctober20,2007ForewordBeginninginthespringof2000,aseriesoffourone-semestercoursesweretaughtatPrincetonUniversitywhosepurposewastopresent,inanintegratedmanner,thecoreareasofanalysis.Theobjectivewastom
5、akeplaintheorganicunitythatexistsbetweenthevariouspartsofthesubject,andtoillustratethewideapplicabilityofideasofanalysistoother¯eldsofmathematicsandscience.Thepresentseriesofbooksisanelaborationofthelecturesthatweregiven.Whilethereareanumberofexcellenttextsdealingwithindividualpartsofwhatwecover,ou
6、rexpositionaimsatadi®erentgoal:pre-sentingthevarioussub-areasofanalysisnotasseparatedisciplines,butratherashighlyinterconnected.Itisourviewthatseeingtheserelationsandtheirresultingsynergieswillmotivatethereadertoattainabetterunderstandingofthesubjectasawhole.Withthisoutcomeinmind,wehaveconcentrated
7、onthemainideasandtheoremsthathaveshapedthe¯eld(sometimessacri¯cingamoresystematicapproach),andwehavebeensensitivetothehistoricalorderinwhichthelogicofthesubjectdeveloped.Wehaveorganizedourexpositionintofour