泛函分析(第6版) YOSIDA 9787506226110 世界图书出版社 pdf epub mobi txt 电子书下载 2025

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出版社：世界图书出版社

ISBN：9787506226110

商品编码：28186512566

出版时间：2010-05-01

具体描述

书名	泛函分析(D16版)
定价	75.00
ISBN	9787506226110
出版社	世界图书出版社
作者	YOSIDA
编号	10830126
出版日期	2010-05-01
印刷日期	2008-11-01
版次	无
字数	无
页数	无

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.