The Biorthogonality Property of Vector-Valued Multivariate Wavelet Packets with M-scale

In this paper, we introduce a class of vector-valued wavelet packets for vector-valued multivariate function space, which are generalizations of univariate wavelet packets. A procedure for constructing a class of biorthogonal vector-valued wavelet packets in higher dimensions is presented and their biorthogonality properties are characterized by virtue of matrix theory, time-frequency analysis method, and operator theory. Three biorthogonality formulas regarding these wavelet packets are derived. Moreover, it is shown how to gain new Riesz bases of space L²(R^s,C^v) from these wavelet packets.