ABSTRACT
In this paper we construct a family of divergence-free multi wavelets. The construction follows Lemarie’s procedure. In the process we find multiresolution analyses (MRA) related by differentiation and integra tion to a family of biorthogonal MRAs constructed by Hardin and Marasovich. The multiscaling and multiwavelets constructed have sym metries and support properties which allow us to obtain biorthogo nal MRAs for the Sobolev space Hq([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 con struct a biorthogonal basis of vector wavelets in (L2([0, l ]2))2 such that the reconstructing wavelets are divergence-free. These functions con stitute a Riesz basis of the L2-Sobolev space of divergence-free square integrable vector fields on the unit square having tangential boundary components.
