Error Bounds for Solving Pseudodifferential Equations on Spheres by Collocation with Zonal Kernels

The problem of solving pseudodifferential equations on spheres by collocation with zonal kernels is considered and bounds for the approximation error are established. The bounds are given in terms of the maximum separation distance of the collocation points, the order of the pseudodifferential operator, and the smoothness of the employed zonal kernel. A by-product of the results is an improvement on the previously known convergence order estimates for Lagrange interpolation.