发表于2024-12-25
泛函分析(第6版) YOSIDA 9787506226110 世界圖書齣版社 pdf epub mobi txt 電子書 下載 2024
書名 | 泛函分析(D16版) |
定價 | 75.00 |
ISBN | 9787506226110 |
齣版社 | 世界圖書齣版社 |
作者 | YOSIDA |
編號 | 10830126 |
齣版日期 | 2010-05-01 |
印刷日期 | 2008-11-01 |
版次 | 無 |
字數 | 無 |
頁數 | 無 |
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(Hormander'sTheorem) 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 |
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. |
泛函分析(第6版) YOSIDA 9787506226110 世界圖書齣版社 pdf epub mobi txt 電子書 下載