Properties of vector-valued multivariable wavelet packets with m-scale

In this paper, we introduce a sort of vector-valued wavelet packets for vector-valued multivariable function space, which are generalizations of univariate wavelet packets. A method for constructing a class of biorthogonal multivariable vector-valued wavelet packets is proposed and their nice properties are discussed by means of operator theory and time-frequency analysis method. The biorthogonality formulas concerning these wavelet packets are derived. Furthermore, it is shown how to draw new Riesz bases of space L²(Rⁿ, C^p) by constructing a series of subspaces of the vector-valued multivariable wavelet packets.