Fourier analysis of 2-point Hermite interpolatory subdivision schemes

Two subdivision schemes with Hermite data on Z are studied These schemes us e 2 or 7 parameters respectively depending on whether Hermite data involve only first derivatives or include second derivatives, For a large region in the parameter space, the schemes are convergent in the space of Schwartz d istributions. The Fourier transform of any interpolating function can be co mputed through products of matrices of order 2 or 3. The Fourier transform is related to a specific system of functional equations whose analytic solu tion is unique except for a multiplicative constant. The main arguments for these results come from Paley-Wiener-Schwartz theorem on the characterizat ion of the Fourier transforms of distributions with compact support and a t heorem of Artzrouni about convergent products of matrices.