A new characterization of convergent multivariate subdivision schemes with nonnegative masks

摘要

We present in this paper new necessary and sufficient conditions for convergence of multivariate subdivision schemes with nonnegative finite masks, which simplify the assertion obtained by Wang in (J Approx Theory 113:207-220, 2001). Moreover, we construct an example, which shows that the convergence behaviors for univariate subdivision schemes and multivariate ones are essentially different.