The properties of a sort of biorthogonal bivariate vector wavelet packets with regard to an integer-valued dilation matrix

In this work, the notion of vector-valued multiresolution analysis of space L²(R²,C^r) is introduced. An approach for designing biorthogonal vector-valued bivariate wavelet packets is presented and their properties are investigated by means of time-frequency analysis method, matrix theory and operator theory. Three biorthogonality formulas regarding the wavelet packets are established. Finally, new Riesz bases of space L²(R²,C^r)are obtained by constructing a series of subspaces composed of these wavelet packets.