An introduction to wavelets
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Cardinal polysplines of order p on annuli are functions in C^2^p^-^2R^n@?0 which are piecewise polyharmonic of order p such that @D^p^-^1S 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.