Generalized Taylor operators and polynomial chains for Hermite subdivision schemes (Q1740508)

In this paper the authors give a new set, called spectral chains, that widely generalize the classical spectral condition and show that these spectral conditions are equivalent tot he existence of a factorization with respect to respective generalized Taylor operators. They conjecture that these factorization can be used to characterized the convergence of Hermite subdivision schemes. \par They define a process that allows them to construct Hermite subdivision schemes of arbitrary regularity. Several numerical examples are given based on B-splines and their derivatives which was one of the first examples of a convergent Hermite subdivision scheme that does not satisfy the spectral condition.