Divergence-free wavelet bases on the hypercube

Given a biorthogonal pair of multi-resolution analyses on the interval, by integration or differentiation, we build a new biorthogonal pair of multi-resolution analyses. Using both pairs, isotropic or, as we focus on, anisotropic divergence-free wavelet bases on the hypercube are constructed. Our construction generalizes the one from [16] by P.G. Lemarié-Rieusset (1992) for stationary multi-resolution analyses on R. It turns out that it requires a specific choice of boundary conditions.