关于指数和的L1范数Littlewood猜想

更新时间:2023-05-20 20:59:15 阅读: 评论:0

Abstract
LetSbeafinitesetofintegersandfs(z)=e2”i”beitsexponentialsum.McGe—
∑础
服饰购hee,Pigno,SmithandKonyaginhaveindependentlyprovedthatFs(x)≥cloglSIforsomeabsoluteconstantC.ThelowerboundhasthecorrectorderofmagnitudeandwasfirstconjecturedbyLittlewood.Inthispaper,wepresentalowerboundsontheL1一normof
exponentialsums.Throughanalysizingthepropertiesofthefunction,n=1andn=2weCPxllgetspoeificintegralvalue.ThuswecanidentifyallabsolutepositiveconstentCSOthatinequalitywasestablished.Byusingthepropertiesofcomplexnumber:Aplural
血塞通颗粒
modeisnolessthantheabsolutevalueofthepluralrealcomponent.Wecanconstruct关于惊蛰的诗
失意的诗句afunction,Wewillbedeformationofinequality.Byconstructingtheinnerproductandnorm,wecalluseFourierseries’knowlegetomanagetheinnerproductandnorm,SOwecan
蛇床子的功效与作用sumsgetanewinequality.theoriginalproblemcanbeconvertedintoseekingexponetial韭菜的营养
平昔
老师快一点oftheflmction’Sabsolutevalue.Inthispaper,thekeystepistoconstructafunction.By
ofthenonpositivesupportandfunctionalapproximation,weusingtherelatedknowlege
cangetalowerboundofthefuntion.Aftercalculation,wecanworkoutaabsolutepositiveconstant,SOthetheoremofLittlewood’Sconjectureisproved
Words:Littlewood’Sconjecture;theFouriercoefficients;theinnerKey
product;normalnumber;nonpositivesupport
II

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