Abstract

The paper considers reduction problems and deformation approaches for nonstationary covariance functions on the (d - 1)-dimensional spheres, Sd-1, embedded in the d-dimensional Euclidean space. Given a covariance function C on Sd-1, we chase a pair (R, Psi), for a function R:[-1,+1] -> R and a smooth bijection Psi, such that C can be reduced to a geodesically isotropic one: C(x, y) = R(), with (., .) denoting the dot product.