A 4-point Hermite subdivision scheme

A subdivision scheme based on 4 points with Hermite data (function and first derivatives) on ZZ is studied. For a large region in the parameter space, the scheme is C-1 convergent or at least is convergent in the space of Schwartz distributions. The Fourier transform of any interpolating function can be computed through products of matrices of order 2. The main tools for proving these results are the Paley-Wiener-Schwartz theorem on the characterization of the Fourier transforms of distributions with compact support, and a theorem of Heil-Colella about the convergence of some products of matrices.