Full rank interpolatory subdivision: a first encounter with the multivariate realm

We extend our previous work on interpolatory vector subdivision schemes to the multivariate case.
As in the univariate case we show that the diagonal and off-diagonal elements of such a scheme have a significantly different structure and that under certain circumstances symmetry of the mask can increase the polynomial reproduction power of the subdivision scheme. Moreover, we briefly point out how tensor product constructions for vector subdivision schemes can be obtained.