Schoenberg coefficients and curvature at the origin of continuous isotropic positive definite kernels on spheres

Ahmed Arafat, Pablo Gregori, Emilio Porcu

We consider the class ${\Psi }_d$ of continuous functions $\psi :[0,\pi ]\to \mathbb{R}$, with $\psi (0)=1$ such that the associated isotropic kernel $C(\xi ,\eta )=\psi (\theta (\xi ,\eta ))$ ---with $ξ,η\in \mat…