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∞ or analytic functions in the ball BR. We prove two main results on the interpolation of C∞ or analytic functions f in the ball BR by polyharmonic functions h of a given order of polyharmonicity p.