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1、SEMICLASSICALANALYSISLawrenceC.EvansandMaciejZworskiDepartmentofMathematicsUniversityofCalifornia,BerkeleyPREFACEThisbookoriginateswithacourseMZtaughtatUCBerkeleyduringthespringsemesterof2003,notesforwhichLCEtookinclass.Inthispresen-tationwehaveprovidedfulldetailsformanyproofsonlysketchedi
2、ntheoriginallectures.Wehavereworkedtheorderofpresentation,addedmany,manyadditionaltopics,andincludedmoreheuristiccommentary.Wehaveaswellintroducedconsistentnotation,recountedinAppendixA.Relevantfunctionalanalysisandotherbackgroundmathematicshavebeenconsoli-datedintoAppendicesB{D.Weshouldme
3、ntionthatseveralexcellenttreatmentsofmathematicalsemiclassicalanalysishaveappearedrecently.Thebook[D-S]byDimassiandSj•ostrandstartswiththeWKB-method,developsthegeneralsemiclas-sicalcalculus,andthenprovideshightechspectralasymptotics.Thepre-sentationofMartinez[M]isbasedonasystematicdevelopm
4、entofFBI(Fourier-Bros-Iagolnitzer)transformtechniques,withapplicationstomi-crolocalexponentialestimatesandtopropagationestimates.Ourtextisintendedasamoreelementary,butbroader,introduction.Exceptforthegeneralsymbolcalculus,wherewefollowedChapter7of[D-S],thereislittleoverlapwiththeseothertwo
5、texts,norwiththein
uentialbookbyRobert[R].GuilleminandSternberg[G-St]o eryetanotherperspectiveonthesubject,verymuchcomplementarytotheonepresentedhere.Theirnotesconcentrateonglobalandfunctorialaspectsofsemiclassicalanaly-sis,inparticularonthetheoryofFourierintegraloperatorsandontraceformula
6、s.WeareespeciallygratefultoHansChristianson,SemyonDyatlov,JustinHolmer,andStephaneNonnenmacherfortheircarefulreadingofearlierversionsofthesenotesandformanyvaluablecommentsandcorrections.34PREFACEOurthanksalsotoFayeYeagerfortypinga rstdraftandtoJonathanDorfmanforTEXadvice.StephenMoyeattheA
7、MSprovideduswithfantastichelpondeeperTEXissues.InhisstudyofsemiclassicalanalysisMZhasbeenin
uencedbyhislongcollaborationwithJohannesSj•ostrand,whomheacknowledgeswithpleasureandgratitude.WewillmaintainonourwebsitesattheUCBerkeleyMathematicsDe-partmentalistoferr
