L ^ρ error estimates for scattered data interpolation on spheres

In this article, working with the sphere Sd embedded in the (d + 1)-dimensional Euclidean space ℝ ^d+1 as the underlying manifold, we obtain an error estimate for interpolating functions f ε Hμ from shifts of a smooth positive definite function defined on Sd , where Hμ is a Sobolev space. We also get an L ^ρ error estimate for f by using a method of Duchon framework.