Covering Numbers of the Unit Ball of Reproducing Kernel Hilbert Space of Zonal Positive Definite Kernels

We present accurate estimates for the covering numbers of the embedding of the Reproducing Kernel Hilbert Space (RKHS) into the space of continuous functions. The RKHS in this work are generated by the Weierstrass fractal kernel and by zonal positive definite kernels on the unit sphere \(\mathbb {S}^d\) where the Fourier coefficients satisfy decay conditions based on the polynomial and exponential type.