Cascade algorithm and multiresolution analysis on the Heisenberg group

In this paper we investigate the relationship between the convergence of cascade algorithm and orthogonal (or biorthogonal) multiresolution analysis on the Heisenberg group. It is proved that the (strong) convergence of cascade algorithm together with the perfect reconstruction condition induces an orthogonal multiresolution analysis and vice versa. Similar results are also proved for biorthogonal multiresolution analysis.