| Abstract: | A comprehensive development of multivariate wavelets along with their duals is presented in this paper. The basic ingredients, such as duality relations, reconstruction and decomposition formulas, and the notion of infinite direct sums, are formulated and established in the general nonorthogonal and multivariate setting. Special emphases include duality criteria and stability conditions. As an application, new results are contributed, particularly in dual wavelets, to the existing literature on low-dimensional wavelets. In addition, the special case when the dilation matrix has determinant 2 is studied in some detail. |
