1)英文原版,PDF书签带目录2)普林斯顿分析系列第4本,泛函分析。
3)经典教材。
ThisisthefourthandfinalvolumeinthePrincetonLecturesinAnalysis,aseriesoftextbooksthataimtopresent,inanintegratedmanner,thecoreareasofanalysis.Beginningwiththebasicfactsoffunctionalanalysis,thisvolumelooksatBanachspaces,Lpspaces,anddistributiontheory,andhighlightstheirrolesinharmonicanalysis.TheauthorsthenusetheBairecategorytheoremtoillustrateseveralpoints,includingtheexistenceofBesicovitchsets.Thesecondhalfofthebookintroducesreaderstoothercentraltopicsinanalysis,suchasprobabilitytheoryandBrownianmotion,whichculminatesinthesolutionofDirichlet'sproblem.TheconcludingchaptersexploreseveralcomplexvariablesandoscillatoryintegralsinFourieranalysis,andillustrateapplicationstosuchdiverseareasasnonlineardispersionequationsandtheproblemofcountinglatticepoints.Throughoutthebook,theauthorsfocusonkeyresultsineachareaandstresstheorganicunityofthesubject.
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