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