Convergence of irregular Hermite subdivision schemes

We consider in this paper the convergence of Hermite subdivision schemes related to the irregular grids X. It is reduced to the convergence of a scalar subdivision scheme, so the results concerning perturbation of convergent scalar subdivision schemes are applied. For interpolatory subdivision schemes HX, with the irregular grid X which is equivalent to the regular grid X∗ in a suitable sense, we proved that the convergence of HX is implied by that of HX∗. Our arguments work in the settings of Lp-convergence and uniform convergence.