Strictly positive definite non-isotropic kernels on two-point homogeneous manifolds: The asymptotic approach (2205.07396v1)

Abstract: We present sufficient condition for a family of positive definite kernels on a compact two-point homogeneous space to be strictly positive definite based on their representation as a series of spherical harmonics. The family analyzed is a generalization of the isotropic kernels and the case of a real sphere is analyzed in details.