Neumann-Bessel级数的Rogosinski型和  

Rogosinski Type Sums of Neumann-Bessel Series

作　　者：成丽波[1] 何甲兴[2] 姜志侠[1] 

机构地区：[1]长春理工大学数学系,长春130022 [2]吉林大学数学研究所,长春130012

出　　处：《吉林大学学报（理学版）》2005年第3期299-302,共4页Journal of Jilin University:Science Edition

摘　　要：由于Neumann Bessel级数的部分和算子S(N,B)n (f;Z)并非对每个连续的函数f(Z)在单位圆周Γ上都一致收敛, 为了改进此插值多项式算子的收敛性, 从Neumann Bessel级数的核函数K(N,B)n (Z,ξ)出发, 对其进行平均, 构造出一个新的Rogosinski核, 并且详细证明了该算子在单位圆周上一致地收敛于每个连续的f(Z), 且具有最佳逼近阶.As the partial sum operator S (N,B) _n(f;Z) of Neumann-Bessel series can not uniformly converge for each continuous f(Z) on unit circle Γ, in order to improve the convergence the operator of interpolation polynomial, the kernel function K (N,B) _n(Z,ξ) of Neumann-Besssl series was divided by 2 to construct a new Rogosinski kernel and it has been proved in detail that such a new operator uniformly converges for any continuous function f(Z) on the unit circle |Z|=1 and has the best approximation order for f(Z) on |Z|=1.

关 键 词：Neumann—Bessel级数 核函数 一致收敛 最佳逼近阶 

分 类 号：O174.41[理学—数学]