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ID:14356401
大小:1.13 MB
页数:176页
时间:2018-07-28
《de reyna j.a. pointwise convergence of fourier series (lnm1785, springer, 2002)(176s)_mcf_》由会员上传分享,免费在线阅读,更多相关内容在学术论文-天天文库。
1、PrefaceThisbookgrewoutofmyattemptinAugust1998tocompareCarleson’sandFefferman’sproofsofthepointwiseconvergenceofFourierserieswithLaceyandThiele’sproofoftheboundednessofthebilinearHilberttransform.IstartedwithCarleson’spaperandsoonrealizedthatmysummervacationwouldnotsufficetounderstandCarleson’sproof.Bit
2、bybitIbegantounderstandit.Iwasimpressedbythebreathtakingproofandstartedtogiveadetailedexpositionthatcouldbeunderstandablebysomeonewho,likeme,wasnotaspecialistinharmonicanalysis.I’vebeenworkingonthisprojectforalmosttwoyearsandlecturedonitattheUniversityofSevillefromFebruarytoJune2000.Thus,thisbookism
3、eantforgraduatestudentswhowanttounderstandoneofthegreatachievementsofthetwentiethcentury.ThisisthefirstexpositionofCarleson’stheoremabouttheconvergenceofFourierseriesinbookform.Itdiffersfromthepreviouslecturenotes,onebyMozzochi[38],andtheotherbyJørsboeandMejlbro[26],inthatourexpositionpointsoutthemoti
4、vationofeverystepintheproof.Sinceitspublicationin1966,thetheoremhasacquiredareputationofbeinganisolatedresult,verytechnical,andnotprofitabletostudy.Therehavealsobeenmanyattemptstoobtaintheresultsbysimplermethods.TothisdayitistheproofthatgivesthefinestresultsaboutthemaximaloperatorofFourierseries.TheCa
5、rlesonanalysisofthefunction,oneofthefundamentalstepsoftheproof,hasaninterestingmusicalinterpretation.Asoundwaveconsistsofaperiodicvariationofpressureoccurringaroundtheequilibriumpressureprevailingataparticulartimeandplace.Thesoundsignalfisthevariationofthepressureasafunctionoftime.TheCarlesonanalysi
6、sgivesthescoreofamusicalcompositiongiventhesoundsignalf.TheCarlesonanalysiscanbecarriedoutatdifferentlevels.Obviouslytheaboveassertionistrueonlyifweconsideranadequatelevel.Carleson’sproofhassomethingthatremindsmeoflivingorganisms.Theproofisbasedonmanychoicesthatseemarbitrary.Thishappensalsoinlivingor
7、ganisms.Anexampleistheerrorinthedesignoftheeyesofthevertebrates.Thephotoreceptorsaresituatedintheretina,buttheiroutputsemergeonthewrongside:insidetheeyes.ThereforetheaxonsmustfinallyVIPrefacebepackedin
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