[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,andHilbertSpacesIbookrootOctober20,2007PrincetonLecturesinAnalysisIFOURIERAN

2、ALYSISanintroductionEliasM.Stein&RamiShakarchiPRINCETONUNIVERSITYPRESSPRINCETONANDOXFORDCopyright©2003byPrincetonUniversityPressPublishedbyPrincetonUniversityPress,41WilliamStreet,Princeton,NewJersey08540IntheUnitedKingdom:PrincetonUniversityPress,6Oxfor

3、dStreet,Woodstock,OxfordshireOX201TWAllRightsReservedLibraryofCongressControlNumber2003103688ISBN978-0-691-11384-5BritishLibraryCataloging-in-PublicationDataisavailableThepublisherwouldliketoacknowledgetheauthorsofthisvolumeforprovidingthecamera-readycop

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

5、ordBeginninginthespringof2000,aseriesoffourone-semestercoursesweretaughtatPrincetonUniversitywhosepurposewastopresent,inanintegratedmanner,thecoreareasofanalysis.Theobjectivewastomakeplaintheorganicunitythatexistsbetweenthevariouspartsofthesubject,andtoi

6、llustratethewideapplicabilityofideasofanalysistoother¯eldsofmathematicsandscience.Thepresentseriesofbooksisanelaborationofthelecturesthatweregiven.Whilethereareanumberofexcellenttextsdealingwithindividualpartsofwhatwecover,ourexpositionaimsatadi®erentgoa

7、l:pre-sentingthevarioussub-areasofanalysisnotasseparatedisciplines,butratherashighlyinterconnected.Itisourviewthatseeingtheserelationsandtheirresultingsynergieswillmotivatethereadertoattainabetterunderstandingofthesubjectasawhole.Withthisoutcomeinmind,we

8、haveconcentratedonthemainideasandtheoremsthathaveshapedthe¯eld(sometimessacri¯cingamoresystematicapproach),andwehavebeensensitivetothehistoricalorderinwhichthelogicofthesubjectdeveloped.Wehaveorganizedourexpositionintofour