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The Characterization of a class of Multivariate Wavelet Packets with an Integer-valued Dilation Matrix

In this paper, the notion of matrix-valued multire-solution-analysis is introduced. A novel way for designing biorthogonal matrix-valued multivariate wavelet packets is presented and their properties are investigated by means of time-frequency analysis method, matrix theory and operator theory. Three biorthogonality formulas concerning these wavelet packets are obtained. Finally, new Riesz bases of three dimensional matrix-valued function space are constructed by designing a series of subspaces of biorthogonal matrix wavelet packets.