Error estimates for interpolation of rough data using the scattered shifts of a radial basis function

The error between appropriately smooth functions and their radial basis function interpolants, as the interpolation points fill out a bounded domain in R-d stop, is a well studied artifact. In all of these cases, the analysis takes place in a natural function space dictated by the choice of radial basis function - the native space. The native space contains functions possessing a certain amount of smoothness. This paper establishes error estimates when the function being interpolated is conspicuously rough.