SPECTRAL CONVERGENCE OF MULTIQUADRIC INTERPOLATION

In this paper, we consider interpolants on h . Z(n) from the closure of the space spanned by translates of the function (\\.\\2 + 1 )beta/2 (beta>-n and n.t an e,en nonnegative integer) along h . Z(n). We show that these interpolants approximate a function, whose Fourier transform satisfies certain asymptotic conditions, up to an error of order h(p), on any compact domain in R(n), where p is only restricted by the smoothness of the function.