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1、LecturesonPartialDifferentialEquationsByG.B.FollandTataInstituteofFundamentalResearchBombay1983LecturesonPartialDifferentialEquationsByG.B.FollandLecturesdeliveredattheIndianInstituteofScience,BangaloreundertheT.I.F.R.–I.I.Sc.ProgrammeinApplicationsofMat
2、hematicsNotesbyK.T.JosephandS.ThangaveluPublishedfortheTataInstituteofFundamentalResearchBombaySpringer-VerlagBerlinHeidelbergNewYork1983AuthorG.B.FollandUniversityofWashingtonSeattle,Washington98175U.S.A.©TataInstituteofFundamentalResearch,1983ISBN3-5
3、40-12280-XSpringer-Verlag,Berlin,Heidelberg.NewYorkISBN0-387-12280-XSpringer-Verlag,NewYork.Heidelberg.BerlinNopartofthisbookmaybereproducedinanyformbyprint,microfilmoranyothermeanswith-outwrittenpermissionfromtheTataInstituteofFundamentalResearch,Colab
4、a,Bombay400005PrintedbyN.S.RayatTheBookCenterLimited,SionEast,Bombay400022andpublishedbyH.Goetze,Springer-Verlag,Heidelberg,WestGermanyPrintedinIndiaPrefaceThisbookconsistsofthenotesforacourseIgaveattheT.I.F.R.CenterinBangalorefromSeptember20toNovember
5、20,1981.ThepurposeofthecoursewastointroducethestudentsintheProgrammeinAppli-cationofMathematicstotheapplicationsofFourieranalysis-bywhichImeanthestudyofconvolutionoperatorsaswellastheFouriertransformitself-topartialdifferentialequations.Facedwiththeprob
6、lemofcover-ingareasonablybroadspectrumofmaterialinsuchashorttime,Ihadtobeselectiveinthechoiceoftopics.Icouldnotdevelopanyonesubjectinareallythoroughmanner;rather,myaimwastopresenttheessentialfeaturesofsometechniquesthatarewellworthknowingandtoderiveafe
7、winterestingresultswhichareillustrativeofthesetechniques.ThisdoesnotmeanthatIhavedealtonlywithgeneralmachinery;indeed,theemphasisinChapter2isonveryconcretecalculationwithdistribu-tionsandFouriertransforms-becausethemethodsofperformingsuchcalculationsar
8、ealsowellworthknowing.Ifthesenotessufferfromthedefectofincompleteness,theypossesthecorrespondingvirtueofbrevity.Theymaythereforebeofvaluetothereaderwhowishestobeintroducedtosomeusefulideaswithouthavingtoploughthroughasystematictreatise.M