Researches into the Biorthogonality Property of Vector-Valued Poly-scale Wavelet Packets in Higher Dimensions
Deyou Yuan, Yong Liu · 2009
We define a class of vector-valued wavelet packets for vector-valued multivariate function space, which are generalizations of univariate wavelet packets. A new approach for constructing a class of biorthogonal vector-valued multivariate wavelet packets is developed and their biorthogonality properties are characterized by means 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(Rs,Cv) from these wavelet packets.