The Biorthogonality Property of the Trivariate Multiwavelet Wraps and Applications in Education Technology and Materials Science

The rise of wavelet analysis in applied mathematics is due to its applications and the flexibility. A sort of multiwavelet wraps with multi-scale dilation factor for space L-2 (R-3, C-1) is introduced, which is the generalization of multivariate wavelet wraps. An approach for designing a sort of biorthogonal rnultiwavelet wraps in three-dimensional space is presented and their biorthogonality property is characterized by virtue of iteration method and time-frequency analysis method. The biorthogonality formulas concerning these wavelet wraps are established. Moreover, it is shown how to obtain new Riesz bases of space L-2 (R-3, C-1) from these wavelet packets.