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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).SuchmaterialsasWeakTopologiesandDualityinLocallyConvexSpaces
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