[分析] fourier analysis an introduction (princeton lectures in analysis, volume 1) elias m. stein, rami shakarchi

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1、IbookrootOctober20,2007FOURIERANALYSISIbookrootOctober20,2007PrincetonLecturesinAnalysisIFourierAnalysis:AnIntroductionIIComplexAnalysisIIIRealAnalysis:MeasureTheory,Integration,andHilbertSpacesIbookrootOctober20,2007PrincetonLecturesinAnalysisIFOURIERANALYSISanintrod

2、uctionEliasM.Stein&RamiShakarchiPRINCETONUNIVERSITYPRESSPRINCETONANDOXFORDCopyright©2003byPrincetonUniversityPressPublishedbyPrincetonUniversityPress,41WilliamStreet,Princeton,NewJersey08540IntheUnitedKingdom:PrincetonUniversityPress,6OxfordStreet,Woodstock,Oxfordshir

3、eOX201TWAllRightsReservedLibraryofCongressControlNumber2003103688ISBN978-0-691-11384-5BritishLibraryCataloging-in-PublicationDataisavailableThepublisherwouldliketoacknowledgetheauthorsofthisvolumeforprovidingthecamera-readycopyfromwhichthisbookwasprintedPrintedonacid-

4、freepaper.∞press.princeton.eduPrintedintheUnitedStatesofAmerica5791086IbookrootOctober20,2007TomygrandchildrenCarolyn,Alison,JasonE.M.S.TomyparentsMohamed&MireilleandmybrotherKarimR.S.IbookrootOctober20,2007ForewordBeginninginthespringof2000,aseriesoffourone-semesterc

5、oursesweretaughtatPrincetonUniversitywhosepurposewastopresent,inanintegratedmanner,thecoreareasofanalysis.Theobjectivewastomakeplaintheorganicunitythatexistsbetweenthevariouspartsofthesubject,andtoillustratethewideapplicabilityofideasofanalysistoother¯eldsofmathematic

6、sandscience.Thepresentseriesofbooksisanelaborationofthelecturesthatweregiven.Whilethereareanumberofexcellenttextsdealingwithindividualpartsofwhatwecover,ourexpositionaimsatadi®erentgoal:pre-sentingthevarioussub-areasofanalysisnotasseparatedisciplines,butratherashighly

7、interconnected.Itisourviewthatseeingtheserelationsandtheirresultingsynergieswillmotivatethereadertoattainabetterunderstandingofthesubjectasawhole.Withthisoutcomeinmind,wehaveconcentratedonthemainideasandtheoremsthathaveshapedthe¯eld(sometimessacri¯cingamoresystematica

8、pproach),andwehavebeensensitivetothehistoricalorderinwhichthelogicofthesubjectdeveloped.Wehaveorganizedourexpositionintofour