A general radial quasi-interpolation operator on the sphere

Geodetic and meteorological data, collected via satellites for example, are genuinely scattered and not confined to any special set of points. In order to learn geodetic and meteorological rules, one needs to use these scattered data only to construct an approximant or interpolant. In this paper, we introduce a general distance generated from the scattered data, and, using this, construct a general radial quasi-interpolation operator on the sphere, and we study the convergence rate of this operator. We also show some potential applications of the results obtained here in satellite geodesy.