泛函分析

图书标准信息

• 作者 K.Yosida 著
• 出版社 世界图书出版公司
• 出版时间 1999-06
• 版次 1
• ISBN 9787506226110
• 定价 75.00元
• 装帧 平装
• 开本 其他
• 纸张 胶版纸
• 页数 500页

【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