【函數的Faler平均逼近】杭州大學.pdf
杭州大学研究生论文稿纸 On Approximation of Functions by EulerMeans Zhu Lai-yi Abstract For agivenseries(A) K=0 ic.lsisdefinedby For a positive number q,we call K=Oa(A) ng k=oK then-th Euler means of the series(A)with the summation indexq.If lim(A)=a,we say the series(A)(E,q)-summable toa.
杭州大学研究生论文稿纸 in thisfield.In view of the convenience we introduce by C2πthe space-Of continuous functions of 2T-period,bllfll=Stfxldx the norm of feL.For f∈ Cx wedefinethek-th order modulusof smoothness offas xA≤ where K!i!(k-j)!In particular,if k=1,w(f,8)denotes the modulus of continuityoff.
杭州大学研究生论文稿纸 fe Hw by u(q,f,x)?We partially resolved this problem.It is the following Theorem2.For a positive integer q,and a given convex modulus of continuity w,we have=(m)In 1960,A.V.Bfimov C²lestima: c(w)by C(w) and obtained the following Theorem EB.