球面带形平移网络逼近的Jackson定理

The Jackson Theorem of Approximation by Zonal Translation Networks on the Unit Sphere

研究了球面带型平移网络逼近阶用球面调和多项式的最佳逼近及光滑模的刻画问题．借助于球调和多项式的最佳逼近多项式和Riesz平均构造出了单位球面Sq上的带形平移网络,并建立了球面带形平移网络对Lp(Sq)中函数一致逼近的Jackson型定理．所得结果表明球面带形平移网络可以达到球调和多项式的逼近阶．

The relationships between the degree of approximation by zonal translation networks and the best approximation of spherical harmonic polynomials as well as the modulus of smoothness are investigated. The zonal translation networks on the unit sphere is constructed with the best approximation of spherical harmonic polynomials and the Riesz means. The Jackson theorem of approximation by such kind of zonal translation is established. The results obtained in the present paper actually imply that the spherical zonal translation network shares the same degree of approximation as the spherical harmonic algebraic polynomials.