球面上Cesàro平均的同收敛算子及其应用(英文)

EQUICONVERGENT OPERATOR OF CESARO MEANS ON SPHERE AND ITS APPLICATIONS

求得一个与球面上Cesaro平均σ_N~δ,它的核形如(N+1)~γP_N^(α,β)(γ=(n-1)/2-δ,α=(n-1)/2+δ,β=(n-3)/2,n是变元数),其中P_N^(α,β)是Jacobi多项式.通过对S_N~δ的研究得到了在一点x处收敛的“反极条件”,即一点-x处必须满足的条件,建立了局部定理,为研究σ_δ~N的收敛性开辟了一条方便的路.

An operator S_N~δ which is equiconvergent with Cesaro means on sphere is given. Its kernel has the form(N+1)~γP_N^(α,β)(γ=(n-1)/2-δ,α=(n-1)/2+δ,β=(n-3)/2, n is the number of variables) where P_N^(α,β)are Jacobi polynomials. By investigating S_N^b the antipole conditions for convergence at a Point x, i. e. the necessary conditions required at the point -x, are obtained. Localization theorems are established. This gives a convenient way to investigate the convergence of Cesaro means on sphere.