Factorization of Hermite subdivision operators preserving exponentials and polynomials (Q503479)

Subdivision schemes are iterative procedures based on repeated application of subdivision operators. Hermite subdivision operators act on vector data which represent function values and consecutive derivatives up to a certain order. In this paper, the authors study how the so-called spectral condition for Hermite subdivision operators extends to spaces \(V_{p,\Lambda}\) generated by monomials \(1\), \(x,\dots,x^p\) and exponentials \(\exp(\pm \lambda_1 x),\dots, \exp(\pm \lambda_r x)\) with \(\Lambda = \{\lambda_1,\dots,\lambda_r\} \subset {\mathbb C}\setminus \{0\}\). The goal of this paper is to understand the preservation of polynomials and exponentials by Hermite subdivision operators. The main tool are annihilator operators that depend only on \(V_{p,\Lambda}\) and on the subdivision level. It is shown that the factorization of a subdivision operator with these preservation properties is strongly connected with such annihilator operators.