The compactly supported cardinal orthogonal vector-valued wavelets with dilation factor α

In this paper, we firstly introduce vector-valued multiresolution analysis with dilation factor α ⩾ 2 and orthogonal vector-valued wavelet. Then, we consider the existence of cardinal compactly supported orthogonal vector-valued wavelet system and describe the characterization of compactly supported orthogonal cardinal vector-valued scaling function and orthogonal vector-valued wavelet. In special, we give some characterizations of cardinal orthogonal vector-valued wavelet system by its mask and symbol in L 2 ( R , C 2 ) . According to Theorems in Section 3, we can conclude algorithm about constructing compactly supported cardinal orthogonal vector-valued wavelet. At last, we give some examples to illustrate our algorithm.