An introduction to wavelets
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Cardinal polysplines of order p on annuli are functions in C2p-2(Rn\{0}) which are piecewise polyharmonic of order p such that Δp-1 S may have discontinuities on spheres in Rn, centered at the origin and having radii of the form ej, 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 ej 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.