Full Rank Positive Matrix Symbols: Interpolation and Orthogonality

We investigate full rank interpolatory vector subdivision schemes whose masks are positive definite on the unit circle except the point z = 1. Such masks are known to give rise to convergent schemes with a cardinal limit function in the scalar case. In the full rank vector case, we show that there also exists a cardinal refinable function based on this mask, however, with respect to a different notion of refinability which nevertheless also leads to an iterative scheme for the computation of vector fields. Moreover, we show the existence of orthogonal scaling functions for multichannel wavelets and give a constructive method to obtain these scaling functions