The Characterization of Biorthogonal Multidimensional Vector Wavelet Wraps with Nine-Scale Dilation Factor
Wavelet analysis is nowadays a widely used tool in applied mathematics. The advantages of wavelet wraps and their promising features in various application have attracted a lot of interest and effort in recent years. In this paper, we develop the notion of a sort of multivariate vector wavelet wraps. A new approcah for designing the multidimensional vector wavelet wraps is formul- ated. Their characters are investigated by virtue of iterative method, time-frequency analysis metho- d and matrix theory. There biorthogonality formulas regarding the wavelet wraps are provided. Biorthogonality decomposition relation formulas of the space L2(Rn)r are obtained by constructing a series of subspaces of the vector-valued wavelet wraps. Moreover, several Riesz bases of space L2(Rn)r are constructed from the wavelet wraps.
Zhihua Xu, Gang Shen and Sally Lin
Z. S. Sheng and Y. M. Yu, "The Characterization of Biorthogonal Multidimensional Vector Wavelet Wraps with Nine-Scale Dilation Factor", Advanced Materials Research, Vols. 171-172, pp. 121-124, 2011