Abstract
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.
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