The Description for Properties of Biorthogonal Vector-Valued Wavelet Packets with Six-Scale Factor

In this work, we introduce a class of vector-valued wavelet packets with six-scale dilation factor for vector-valued higher dimensional function space. The definition of biorthogonal vector-valued mul dimensional wavelet packets is proposed and their biorthogonality properties are investigated by virtue of matrix theory, time-frequency analysis method, and operator theory. Three biorthogonality formulas regarding these wavelet packets are established. Moreover, it is shown how to gain new Riesz bases of space L
²
(R
^u
, C
^v
) from these wavelet packets.