Regularity of multiwavelets (Q1371970)

The authors study the regularity of vector fields \(f:\mathbb{R}\to \mathbb{R}^N\) which are the solutions of a vector refinement equation: \(f= \sum_{k\in\mathbb{Z}} A^T_kf(2.-k)\), where \((A^T_j, j\in\mathbb{Z})\) is a finitely supported bi-infinite vector of \(N\times N\) matrices. They approach this problem by investigating the interplay between different concepts of subdivision schemes. They give in the last section an application to the construction of multiwavelets of arbitrary regularity.