ABSTRACT
P. G. Lemarie-Rieusset introduced a technique for constructing biorthogo nal pairs of compactly supported wavelets, such that one of the generators is divergence-free. Lemarie’s construction is based on the existence of biorthog onal MRAs related by differentiation and integration (see [5]), which, as we just showed, applies to multiwavelets as well. We will quickly recall for the reader the steps in the construction of a biorthogonal basis of divergence-free multiwavelets for the particular HM multiwavelets discussed in the previous sections. We will restrict ourselves in this paper to dimension 2. The other interesting case for applications is dimension 3. The construction in all di mensions and for form-valued multiwavelets is presented in [8] when starting with an orthogonal MRA of multiplicity r. One can reproduce almost ver batim this result in the biorthogonal case, as long as the transition matrices can be chosen to be M and —M*, as is the case in the modified HardinMarasovich MRA.
