analysis-[treatise.on.analysis.vol-v].(j.dieudonne)

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1、TREATISEONANALYSISVolumeVThisisVolume10-VinPUREANDAPPLIEDMATHEMATICSASeriesofMonographsandTextbooksEditors:SAMUELEILENBERGANDHYMANBASSAlistofrecenttitlesinthisseriesappearsattheendofthisvolume.Volume10TREATISEONANALYSIS10-1.ChaptersI-XI,FoundationsofModern

2、Analysis,enlargedandcorrectedprinting,196910-11.ChaptersXII-XV,enlargedandcorrectedprinting,197610-111.ChaptersXVI-XVII,197210-IV.ChaptersXVIII-XX,197410-V.ChapterXXI,1977TREATISEONANALYSISJ.DIEUDONN€MembredeI’InstitutVolumeVTranslatedby1.G.MacdonaldQueenM

3、aryCollegeUniversityofLondonACADEMICPRESSNewYorkSanFranciscoLondon1977ASubsidiaryofHarcourtBraceJovanovich,PublishersCOPYRIGHT01977,BYACADEMICPRESS,INC.ALLRIGHTSRESERVED.NOPARTOFTHISPUBLICATIONMAYBEREPRODUCEDORTRANSMITTEDINANYFORMORBYANYMEANS,ELECTRONICORM

4、ECHANICAL,INCLUDINGPHOTOCOPY,RECORDING,ORANYINFORMATIONSTORAGEANDRETRIEVALSYSTEM,WITHOUTPERMISSIONINWRITINGFROMTHEPUBLISHER.ACADEMICPRESS,INC.111FifthAvenue,NewYork.NewYork10003UnitedKingdomEditionpublishedbyACADEMICPRESS,INC.(LONDON)LTD.24/28OvalRoad.Lond

5、onNW1LibraryofCongressCataloginginPublicationData(Revised)Dieudonne,JeanAlexandre,DateTreatiseonanalysis.(Pureandappliedmathematics,aseriesofmonographsandtextbooks;10)Exceptforv.1,atranslationofElementsd’analyse.Vols.2-translatedbyI.G.MacDonald.Includesvar

6、iouseditionsofsomevolumes.Includesbibliographiesandindexes.1.Mathematicalanalysis-Collectedworks.I.Title.11.Series.QA3.P8vol.10,1969510’.8s[515]75-313532ISBN0-12-215505-X(v.5)PRINTEDINTHEUNITEDSTATESOFAMERICA“TreatiseonAnalysis,”VolumeVFirstqublishedintheF

7、renchLanguageunderthetitle“Eltmentsd’Analyse,’:tome5andcopyrightedin1975byGauthier-Villars,Editeur,Paris,France.CONTENTSNotation...........................viiChapterXXICOMPACTLIEGROUPSANDSEMISIMPLELIEGROUPS.....1I.Continuousunitaryrepresentationsoflocallyc

8、ompactgroups2.TheHilbertalgebraofacompactgroup3.Charactersofacompactgroup4.Continuousunitaryrepresentationsofcompactgroups5.Invariantbilinearforms;theKillingform6.SemisimpleLiegroups.Criterionofsemisimplicity