球面Jackson多项式逼近的正逆定理  

The Direct and Inverse Theorem of Approximation for Jackson Polynomials on the Sphere

作　　者：熊静宜[1] 曹飞龙[1] 杨汝月[1] 

机构地区：[1]中国计量学院理学院,杭州310018

出　　处：《数学年刊（A辑）》2011年第2期205-212,共8页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.60873206)资助的项目

摘　　要：研究了球面Jackson多项式J_(v,s)f的逼近阶,建立了该多项式逼近的强型正向与逆向不等式.利用球面光滑模较好地刻画了Jackson多项式的逼近性能,证明了存在与v和f无关的常数C_1和C_2,使得对于定义在球面上任意p-幂勒贝格可积或连续函数f成立C_1ω(f,1/v)_p≤‖J_(v,s)f-f‖_p≤C_2ω(f,1/v)_p,其中ω(f,t)p是f的光滑模.Abstract The degree of approximation for the Jackson polynomials Jv,sf on the unit sphere is considered. The direct and inverse inequalities of strong type for approximation by these polynomials are established. The approximation behavior of these polynomials is nicely characterized by using modulus of smoothness of sphere. Namely, it is proved that there exist constants C1 and C2 independent of v and f such that for any p power Lebesgue integrable or continuous function f defined on the sphere, where ω（f, t）p is the modulus of smoothness of f.

关 键 词：球面 Jackson多项式 逼近 光滑模 下界 

分 类 号：O174.41[理学—数学]