A study of multiple vector-valued wavelet packets associated with a dilation matrix in higher dimensions

In this paper, the notion of multiple vector-valued multiresolution analysis of space L
²
(R
^s
,C
^r×r
) is introduced. A method for constructing biorthogonal multiple vector-valued wavelet packets in higher dimensions is presented and their properties is 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 space L
²
(R
^s
,C
^r×r
) is obtained by constructing a series of subspaces of biorthogonal vector-valued wavelet packets.