Convergence of Hermite interpolatory operators

Divergence-free wavelets play important roles in both partial differential equations and fluid mechanics. Many constructions of those wavelets depend usually on Hermite splines. We study several types of convergence of the related Hermite interpolatory operators in this paper. More precisely, the uniform convergence is firstly discussed in the second part; then, the third section provides the convergence in the Donoho's sense. Based on these results, the last two parts are devoted to show the convergence in some Besov spaces, which concludes the completeness of Bittner and Urban's expansions.