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泛函分析

泛函分析
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作者: 著
出版社: 世界图书出版公司
1999-06
版次: 1
ISBN: 9787506226110
定价: 75.00
装帧: 平装
开本: 其他
纸张: 胶版纸
页数: 500页
分类: 自然科学
66人买过
  • hepresentbookisbasedonlecturesgivenbytheauthorattheUniversityofTokyoduringthepasttenyears.ItisintendedasatextbooktobestudiedbystudentsontheirownortobeusedinacourseonFunctionalAnalysis,i.e.,thegeneraltheoryoflinearoperatorsinfunctionspacestogetherwithsalientfeaturesofitsapplicationtodiversefieldsofmodemandclassicalanalysis.Necessaryprerequisitesforthereadingofthisbookaresummarized,withorwithoutproof,inChapter0undertitles：SetTheory,TopologicalSpaces,MeasureSpacesandLinearSpaces.Then,startingwiththechapteronSemi-norms,ageneraltheoryofBanachandHilbertspacesispresentedinconnectionwiththetheoryofgeneralizedfunctionsofS.L.SOBOLEVandL.SCHWARTZ.Whilethebookisprimarilyaddressedtograduatestudents,itishopeditmightproveusefultoresearchmathematicians,bothpureandapplied.Thereadermaypass,e.g.,fromChapterIX(AnalyticalTheory.ofSemi-groups)directlytoChapterXIII(ErgodicTheoryandDiffusionTheory)andtoChapterXIV(IntegrationoftheEquationofEvolution).Suchmaterialsas"WeakTopologiesandDualityinLocallyConvexSpaces"and"NuclearSpaces"arepresentedintheformoftheappendicestoChapterVandChapterX,respectively.Thesemightbeskippedforthefirstreadingbythosewhoareinterestedratherintheapplicationoflinearoperators. Contents
    0.Preliminaries
    1.SetTheory
    2.TopologicalSpaces
    3.MeasureSpaces
    4.LinearSpaces
    I.Semi-nonns
    1.Semi-nonnsandLocallyConvexLinearTopologicalSpaces
    2.NonnsandQuasi-nonns
    3.ExamplesofNormedLinearSpaces
    4.ExamplesofQuasi-nonnedLinearSpaces
    5.Pre-HilbertSpaces
    6.ContinuityofLinearOperators
    7.BoundedSetsandBomologicSpaces
    8.GeneralizedFunctionsandGeneralizedDerivatives
    9.B-spacesandF-spaces
    10.TbeCompletion
    11.FactorSpacesofaB-space
    12.ThePartitionofUnity
    13.GeneralizedFunctionswithCompactSupport
    14.TheDirectProductofGeneralizedFunctions
    II.ApplicationsoftheBaire-HausdorffTheorem
    1.TheUnifonnBoundednessTheoremandtheResonanceTheorem
    2.TheVitali-Hahn-SaksTheorem
    3.TheTermwiseDifferentiabilityofaSequenceofGeneralizedFunctions
    4.ThePrincipleottheCondensationofSingularities
    5.TheOpenMappingTheorem
    6.TheClosedGraphTheorem
    7.AnApplicationoftheClosedGraphTheorem(HormandersTheorem)
    III.TheOrthogonalProjectionandF.RieszRepresentationTheo-rem
    1.TheOrthogonalProjection
    2."NearlyOrthogonal"Elements
    ……
    IV.TheHahn-BanachTheorems
    V.StrongConvergenceandWeakConvergence
    VI.FourierTransformandDifferentialEquations
    VII.DualOperators
    VIII.ResolventandSpectrum
    IX.AnalyticalTheoryofSemi-groups
    XCompactOperators
    XI.NonnedRingsandSpectralRepresentation
    XII.OtherRepresentationTheoremsinLinearSpaces
    XIIT.ErgodicTheoryandDiffusionTheory
    XIVTheIntegrationoftheEquationofEvolution
    SupplementaryNotes
    Bibliography
    Index
    NotationofSpaces
  • 内容简介:
    hepresentbookisbasedonlecturesgivenbytheauthorattheUniversityofTokyoduringthepasttenyears.ItisintendedasatextbooktobestudiedbystudentsontheirownortobeusedinacourseonFunctionalAnalysis,i.e.,thegeneraltheoryoflinearoperatorsinfunctionspacestogetherwithsalientfeaturesofitsapplicationtodiversefieldsofmodemandclassicalanalysis.Necessaryprerequisitesforthereadingofthisbookaresummarized,withorwithoutproof,inChapter0undertitles：SetTheory,TopologicalSpaces,MeasureSpacesandLinearSpaces.Then,startingwiththechapteronSemi-norms,ageneraltheoryofBanachandHilbertspacesispresentedinconnectionwiththetheoryofgeneralizedfunctionsofS.L.SOBOLEVandL.SCHWARTZ.Whilethebookisprimarilyaddressedtograduatestudents,itishopeditmightproveusefultoresearchmathematicians,bothpureandapplied.Thereadermaypass,e.g.,fromChapterIX(AnalyticalTheory.ofSemi-groups)directlytoChapterXIII(ErgodicTheoryandDiffusionTheory)andtoChapterXIV(IntegrationoftheEquationofEvolution).Suchmaterialsas"WeakTopologiesandDualityinLocallyConvexSpaces"and"NuclearSpaces"arepresentedintheformoftheappendicestoChapterVandChapterX,respectively.Thesemightbeskippedforthefirstreadingbythosewhoareinterestedratherintheapplicationoflinearoperators.
  • 目录:
    Contents
    0.Preliminaries
    1.SetTheory
    2.TopologicalSpaces
    3.MeasureSpaces
    4.LinearSpaces
    I.Semi-nonns
    1.Semi-nonnsandLocallyConvexLinearTopologicalSpaces
    2.NonnsandQuasi-nonns
    3.ExamplesofNormedLinearSpaces
    4.ExamplesofQuasi-nonnedLinearSpaces
    5.Pre-HilbertSpaces
    6.ContinuityofLinearOperators
    7.BoundedSetsandBomologicSpaces
    8.GeneralizedFunctionsandGeneralizedDerivatives
    9.B-spacesandF-spaces
    10.TbeCompletion
    11.FactorSpacesofaB-space
    12.ThePartitionofUnity
    13.GeneralizedFunctionswithCompactSupport
    14.TheDirectProductofGeneralizedFunctions
    II.ApplicationsoftheBaire-HausdorffTheorem
    1.TheUnifonnBoundednessTheoremandtheResonanceTheorem
    2.TheVitali-Hahn-SaksTheorem
    3.TheTermwiseDifferentiabilityofaSequenceofGeneralizedFunctions
    4.ThePrincipleottheCondensationofSingularities
    5.TheOpenMappingTheorem
    6.TheClosedGraphTheorem
    7.AnApplicationoftheClosedGraphTheorem(HormandersTheorem)
    III.TheOrthogonalProjectionandF.RieszRepresentationTheo-rem
    1.TheOrthogonalProjection
    2."NearlyOrthogonal"Elements
    ……
    IV.TheHahn-BanachTheorems
    V.StrongConvergenceandWeakConvergence
    VI.FourierTransformandDifferentialEquations
    VII.DualOperators
    VIII.ResolventandSpectrum
    IX.AnalyticalTheoryofSemi-groups
    XCompactOperators
    XI.NonnedRingsandSpectralRepresentation
    XII.OtherRepresentationTheoremsinLinearSpaces
    XIIT.ErgodicTheoryandDiffusionTheory
    XIVTheIntegrationoftheEquationofEvolution
    SupplementaryNotes
    Bibliography
    Index
    NotationofSpaces
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