A function ρ : [0,∞)→ (0,1] is a completely monotonic function if and only if ρ(‖x‖) is positive definite on R for all d and thus it represents the correlation function of a weakly stationary and isotropic Gaussian random field. Radial positive definite functions are also of importance as they represent characteristic functions of spherically symmetric probability distributions. In this paper, ...

The modeling of spatio-temporal processes is crucial in many fields such as environmental science, hydrology, and water storage engineering. A basic concept the model an auto-covariance function. stream network based on Euclidean distance function for investigating river pollution will potentially face a serious accuracy problem, due to material or pollutant movement only occurring within trave...

We consider interpolation methods defined by positive definite functions on a compact group. Estimates for the smallest and largest eigenvalue of the interpolation matrix in terms of the localization of the positive definite function on G are presented and we provide a method to get positive definite functions explicitly on compact semisimple Lie groups. Finally we apply our results to construc...