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M.Reed 、B.Simon 编 / 世界图书出版公司 / 2003-06 / 平装
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现代数学物理方法(第1卷):泛函分析
Thisbookisthefirstofamultivolumeseriesdevotedtoanexpositionoffunctionalanalysismethodsinmodemmathematicalphysics.Itdescribesthefundamentalprinciplesoffunctionalanalysisandisessentiallyself-contained,althoughthereareoccasionalreferencestolatervolumes.Wehaveincludedafewapplicationswhenwethoughtthattheywouldprovidemotivationforthereader.Latervolumesdescribevariousadvancedtopicsinfunctionalanalysisandgivenumerousapplicationsinclassicalphysics,modemphysics,andpartialdifferenrialequations.
PrefaceIntroductionContentsofOtherVolumesI:PRELIMINARIES1.Setsandfunctions2.MetricandnormedlinearspacesAppendixLirasupandliminf3.TheLebesgueintegral4.Abstractmeasuretheory5.Twoconrergencearguments6.EquicontinuityNotesProblemsII:HILBERTSPACES1.ThegeometryofHilbertspace2.TheRieszlemma3.Orthonormalbases4.TensorproductsofHilbertspaces5.Ergodictheory:anintroductionNotesProblemsIII:BANACHSPACES1.Definitionandexamples2.Dualsanddoubleduals3.TheHahn-Banachtheorem4.OperationsonBanachspaces5.TheBairecategorytheoremanditsconsequencesNotesProblemsIV:TOPOLOGICALSPACES1.Generalnotions2.NetsandConvergence3.CompactnessAppendixTheStone-Weierstrasstheorem4.MeasuretheoryonCompactspaces5.WeaktopologiesonBanachspacesAppendixWeakandstrongmeasurabilityNotesProblemsV:LOCALLYONVEXSPACES1.Generalproperties2.Frdchetspaces3.FunctionsofrapiddeceaseandthetempereddistributionsAppendixTheN-representationforand4.Inductivelimits:generalizedfunctionsandweaksolutionsofpartialdifferentialequations5.Fixedpointtheorems6.Applicationsoffixedpointtheorems7.Topologiesonlocallyconvexspaces:dualitytheoryandthestrongdualtopologyAppendixPolarsandtheMackey-ArenstheoremNotesProblemsVI:BOUNDEDOPERATORSVII:THESPECTRALTHEOREMVIII:UNBOUNDEDOPERATORSTHEFOURIERTRANSFORMSUPPLEMENTARYMATERIALListofSymbols
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