The Convergence Rate for a K-Functional in Learning Theory

It is known that in the field of learning theory based on reproducing kernel Hilbert spaces the upper bounds estimate for a K-functional is needed. In the present paper, the upper bounds for the K-functional on the unit sphere are estimated with spherical harmonics approximation. The results show that convergence rate of the K-functional depends upon the smoothness of both the approximated function and the reproducing kernels