Simultaneous approximations for functions in Sobolev spaces by derivativesof polyharmonic cardinal splines

We prove in this paper that functions in Sobolev spaces and their derivativ es can be approximated by polyharmonic splines and their derivatives in L-p (R-n) norms. Of particular interest are the remainder formulas of such appr oximations and the order of convergence by the derivatives of cardinal poly harmonic interpolational splines. (C) 1999 Academic Press.