Factorization of Hermite subdivision operators preserving exponentials and polynomials

In this paper we focus on Hermite subdivision operators that act on vector valued data interpreting their components as function values and associated consecutive derivatives. We are mainly interested in studying the exponential and polynomial preservation capability of such kind of operators, which can be expressed in termsof a generalization of the spectral condition property in the spaces generated bypolynomials and exponential functions. The main tool for our investigation are convolution operators that annihilate the aforementioned spaces, which apparently is ageneral concept in the study of various types of subdivision operators. Based on these annihilators, we characterize the spectral condition in terms of factorization of thesubdivision operator.