Construction of biorthogonal multiwavelets

There are perfect formulas for the constructions of biorthogonal uniwavelets. Let φ(x) = k∈Z pkφ(2x − k), φ˜(x) = k∈Z p˜kφ˜(2x − k) be a pair of biorthogonal uniscaling functions, then a pair of biorthogonal uniwavelet associated with the above biorthogonal uniscaling functions can be easily expressed as ψ(x) = k∈Z (−1)k−1 p˜1−kφ(2x − k), ψ˜ (x) = k∈Z (−1)k−1p1−kφ˜(2x − k). However, it seems that there is not such a good formula of similar structure for biorthogonal multiwavelets. In this paper, we will give a procedure for constructing compactly supported biorthogonal multiwavelets, which makes construction of biorthogonal multiwavelets easy like in the construction of biorthogonal uniwavelet. Our approach is also suitable for the case of compactly supported orthogonal multiwavelets. Four examples for constructing multiwavelets are given.  2002 Elsevier Science (USA). All rights reserved.