Continuous and discrete least-squares approximation by radial basis functions on spheres

In this paper we discuss Sobolev bounds on functions that vanish at scattered points on the n-sphere Sn in Rn+1. The Sobolev spaces involved may have fractional as well as integer order. We then apply these results to obtain estimates for continuous and discrete least-squares surface fits via radial basis functions (RBFs). We also address a stabilization or regularization technique known as spline smoothing.