ON APPROXIMATION BY SPHERICAL ZONAL TRANSLATION NETWORKS BASED ON BOCHNER-RIESZ MEANS

摘要

A sequence of spherical zonal translation networks based on the Bochner-Riesz means of spherical harmonics and the Riesz means of Jacobi polynomials is introduced,and its degree of approximation is achieved. The results obtained in the present paper actually imply that the approximation of zonal translation networks is convergent if the action functions have certain smoothness.