The Characterization of a Kind of Vector-Valued Multivariate Wavelet Packets with Composite Dilation Matrix
In this article, the notion of a kind of multivariate vector-valued wavelet packets with composite dilation matrix is introduced. A new method for designing a kind of biorthogonal vector- valued wavelet packets in higher dimensions is developed and their biorthogonality property is inv- -estigated by virtue of matrix theory, time-frequency analysis method, and operator theory. Two biorthogonality formulas concerning these wavelet packets are presented. Moreover, it is shown how to gain new Riesz bases of space by constructing a series of subspace of wavelet packets.
Y. H. Xia and H. Li, "The Characterization of a Kind of Vector-Valued Multivariate Wavelet Packets with Composite Dilation Matrix", Key Engineering Materials, Vols. 439-440, pp. 932-937, 2010