Convergence of Vector Subdivision Schemes in Sobolev Spaces,

In this paper we consider functional equations of the form Φ=∑α∈Zsa(α)Φ(M·−α), where Φ=(φ1,…,φr)T is an r×1 vector of functions on the s-dimensional Euclidean space, a(α), α∈Zs, is a finitely supported sequence of r×r complex matrices, and M is an s×s isotropic integer matrix such that limn→∞M−n=0. We are interested in the question, for w...More