Cardinal interpolation with polysplines on annuli

Abstract

Cardinal polysplines of order p on annuli are functions in C 2p−2 (R n \{0}) which are piecewise polyharmonic of order p such that ∆ p−1 S may have discontinuities on spheres in R n, centered at the origin and having radii of the form e j,j ∈ Z. The main result is an interpolation theorem for cardinal polysplines where the data are given by sufficiently smooth functions on the spheres of radius e j and center 0 obeying a certain growth condition in |j|. This result can be considered as an analogue of the famous interpolation theorem of Schoenberg for cardinal splines. Key words: Cardinal splines, Schoenberg interpolation theorems, L−splines, cardinal spline interpolation, spherical harmonics, polyharmonic functions i