The Jackson Theorem of Approximation by Zonal Translation Networks on the Unit Sphere
Baohuai Sheng · Advances in Mathematics · 2006
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.