Covering number of the unit ball of Reproducing Kernel Hilbert Space of Schoenbergs kernels - Gonzalez, Karina Navarro (2023)
In this work, we present accurate upper and lower bounds for the entropy/covering numbers of the unit ball for two general classes of Reproducing Kernel Hilbert Space (RKHS) on the unit sphere of Rd+1. In both classes, the RKHS is generated by an Schoenberg type kernel, it means, a positive definite continuous and zonal kernel. The upper and lower bounds we present carry precise information about the asymptotic constants, depending on the dimension of the sphere and the monotonic behavior of the Schoenberg/Fourier coefficients of the kernel we work with.