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The concept of symmetric recursive algorithm leads to new, sdimensional spline spaces. We present a general scheme for constructing a collection of multivariate S-splines with k-l continuous derivatives whose linear span contains all polynomials of degree at most k . This scheme is different from the one developed earlier by Dahmen and Micchelli and, independently, by Höllig, which was based on combinatorial principles and the geometric interpretation of the ß-spline. The new spline spacedoi:10.1090/s0025-5718-1992-1134724-1 fatcat:pqlgmcaokjetrh7f3xtlf6pkty