Divergence-free Multiwavelets on Rectangular Domains

In this paper we construct a family of divergence-free multiwavelets. The construction follows Lemari e's procedure. In the process we nd multiresolution analyses (MRA) related by diierentiation and integration to a family of biorthogonal MRAs constructed by Hardin and Marasovich. The multiscaling and multiwavelets constructed have symmetries and support properties which allow us to obtain biorthog-onal MRAs for the Sobolev space H 1 0 ((0; 1]), just by truncating the smoothened scaling functions and wavelets, and keeping those functions that have zero boundary values. These are the building blocks to construct a biorthogonal basis of vector wavelets in (L 2 ((0; 1] 2)) 2 such that the reconstructing wavelets are divergence-free. These functions constitute a Riesz basis of the L 2-Sobolev space of divergence-free square integrable vector elds on the unit square having tangential boundary components.