On polyharmonic interpolation

In the present paper we will introduce a new approach to multivariate interpolation by employing polyharmonic functions as interpolants, i.e. by solutions of higher order elliptic equations. We assume that the data arise from C-infinity or analytic functions in the ball B-R. We prove two main results on the interpolation of C-infinity or analytic functions f in the ball B-R by polyharmonic functions h of a given order of polyharmonicity p. (c) 2006 Elsevier Inc. All rights reserved.