Deslauriers, G. & Dubuc, S. Constr. Approx (1989) 5: 49. doi:10.1007/BF01889598
Using a baseb and an even number of knots, we define a symmetric iterative interpolation process. The main properties of this process come from an associated functionF. The basic functional equation forF is thatF(t/b)=σnF(n/b)F(t-n). We prove thatF is a continuous positive definite function. We find almost precisely in which Lipschitz classes derivatives ofF belong. If a functiony is defined only on integers, this process extendsy continuously to the real axis asy(t=∑ny(n)F(t−n). Error bounds for this iterative interpolation are given.