Construction of a class of compactly supported orthogonal vector-valued wavelets

In this paper, first we introduce vector-valued multiresolution analysis with dilation factor α ⩾ 2 and orthogonal vector-valued wavelet. A necessary and sufficient condition on the existence of orthogonal vector-valued wavelet is derived. Then, for a given L-length compactly supported orthogonal vector-valued wavelet system, by virtue of an s × s orthogonal real matrix M and an s × s symmetry idempotent real matrix H where M(Is − H + H e−iη) is a unitary matrix for each η ∈ R, we construct (L + 1)-length compactly supported orthogonal vector-valued wavelet system. Our method is of flexibility and easy to carry out. Finally, as an application we give an example.