Simultaneous Approximations for Functions in Sobolev Spaces by Derivatives of Polyharmonic Cardinal Splines

Abstract

We prove in this paper that functions in Sobolev spaces and their derivatives can be approximated by polyharmonic splines and their derivatives in Lp(Rn) norms. Of particular interest are the remainder formulas of such approximations and the order of convergence by the derivatives of cardinal polyharmonic interpolational splines.