【算子逼近与正系数多项式逼近中的几个问题】.pdf

【算子逼近与正系数多项式逼近中的几个问题】.pdf

算子逼近与正系数多项 式逼近中的几个问题 许贵桥 一九九0.五.二十.SomeProblemsaboutApproximatiorofUperators andPositiveoefficientFolynomials XiGueiviao ABSTRACT his paper consists of turee cnapters.In chaoter1we obtainaKorovkint/peuroxiinationtheoremforset-valued maps.Inchaptr2weconsider tneproblemof degreeof approxdmation(under wei.newmethodtoprove Theorem1Letbea se:-reciprocaispaceandlet to clo,1],].In order that rF-.F for each rec[,1],é],it is necessaryand sufficientthatTF-.F,for any r(t)=A,where Ae,nAll=1.Let k=m=C0s 2k-1 be tne zeros of r(x)=cosnθ,(x=coso),the nth degree Tcheby- n Hn(f,x)= k=1 where bk(x)=(1-xx)(hk