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

Abstract 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 ( I s  −  H  +  H  e −i η ) 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.