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On Lie Groups and Representations of Locally Compact Groups

On Lie Groups and Representations of Locally Compact Groups

ID：40391258

大小：606.99 KB

页数：140页

时间：2019-08-01

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1、LecturesonLieGroupsandRepresentationsofLocallyCompactGroupsByF.BruhatTataInstituteofFundamentalResearch,Bombay1958(Reissued1968)LecturesonLieGroupsandRepresentationsofLocallyCompactGroupsByF.BruhatNotesbyS.RamananNopartofthisbookmaybereproducedinanyformbyprint,microfilmoranyothermeanswith-outwrittenp

2、ermissionfromtheTataInstituteofFundamentalResearch,Colaba,Bombay5TataInstituteofFundamentalResearch,Bombay1958(Reissued1968)IntroductionWeshallconsidersomeheterogeneoustopicsrelatingtoLiegroupsandthegeneraltheoryofrepresentationsoflocallycompactgroups.Thefirstpartexclusivelydealswithsomeelementaryfac

3、tsaboutLiegroupsandthelasttwopartsareentirelyindependentofthematerialcontainedinthefirst.Wehaverigidlyadheredtotheanalyticapproachinestab-lishingtherelationsbetweenLiegroupsandLiealgebras.Thuswedonotneedthetheoryofdistributionsonamanifoldortheexistenceofintegralmanifoldsforaninvolutorydistribution.Th

4、esecondpartconcernsitselfonlywiththegeneraltheoryofmea-suresonalocallycompactgroupandrepresentationsingeneral.Onlyapassingreferenceismadetodistributions(inthesenseofL.Schwartz),andinducedrepresentationsarenottreatedindetail.Inthethirdpart,wefirstconstructthecontinuoussum('thedirectintegral')ofHilbert

5、spacesandthendecomposeaunitaryrepresenta-tionsintoacontinuoussumofirreduciblerepresentations.WederivethePlancherelformulaforaseparableunimodulargroupintermsoffactorialrepresentationsandderivetheclassicalformulaintheabeliancase.iiiContentsIntroductioniiiILieGroups11Topologicalgroups32LocalstudyofLieg

6、roups93RelationsbetweenLiegroupsandLiealgebras-I194RelationbetweenLiegroupsandLiealgebras-II31IIGeneralTheoryofRepresentations475Measuresonlocallycompactspaces476Convolutionofmeasures537Invariantmeasures618RegularRepresentations739Generaltheoryofrepresentations83vviContentsIIIContinuoussumofHilbertS

7、paces8910ContinuoussumofHilbertSpaces-I9111ContinuoussumofHilbertspaces-II10312ThePlancherelformula115Bibliography127PartILieGroups1Chapter1Topologicalgroups1.1Wehereassemblesomeresultsontopologicalgr

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