Spectral convergence of multiquadric interpolation

In this paper, we consider interpolants on h.Z” from the closure of the space spanned by translates of the function [formula omitted] and not an even nonnegative integer) along h.Zn. We show that these interpolants approximate a function, whose Fourier transform satisfies certain asymptotic conditions, up to an error of order hp on any compact domain in Rn where p is only restricted by the smoothness of the function.