The properties of a class of biorthogonal vector-valued nonseparable bivariate wavelet packets

In this paper, we introduce a class of vector-valued wavelet packets of space L2(R2,Cκ)L2(R2,Cκ), which are generalizations of multivariate 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(R2,Cκ)L2(R2,Cκ) from these wavelet packets. Relation to some physical theories such as the Higgs field is also discussed.