Multiwavelet frames from refinable function vectors

Starting from any two compactly supported d-refinable function vectors in (L-2(R))(r) with multiplicity r and dilation factor d, we show that it is always possible to construct 2rd wavelet functions with compact support such that they generate a pair of dual d-wavelet frames in L-2(R) and they achieve the best possible orders of vanishing moments. When all the components of the two real-valued d-refinable function vectors are either symmetric or antisymmetric with their symmetry centers differing by half integers, such 2rf wavelet functions, which generate a pair of dual d-wavelet frames, can be real-valued and be either symmetric or antisymmetric with the same symmetry center. Wavelet frames from any d-refinable function vector are also considered. This paper generalizes the work in [5,12,13] on constructing dual wavelet frames from scalar refinable functions to the multiwavelet case. Examples are provided to illustrate the construction in this paper.