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The characters of a sort of multidimensional wavelet wraps concerning an integer-valued dilation matrix

The rise of frame theory in applied mathematics is due to the flexibility and redundancy of frames. The notion of a generalized multiresolution structure of L2(R) is proposed. In this paper, the notion of matrix-valued multiresolution analysis of space L2(Rs,Cr)is introduced. A method for constructing biorthogonal vector-valued multidimensional wavelet packets is developed and their properties are discussed by means of time-frequency analysis method, matrix theory and operator theory. Three biorthogonality formulas concerning these wavelet wraps are obtained. Finally, new Riesz bases of space L2(Rs,Cr) is obtained by constructing a series of subspaces of biorthogonal vector-valued wavelet wraps.