Joint dilation scaling sets on the reducing subspaces

Abstract

In this paper, we study joint dilation scaling sets, MSF multiwavelets and non-MSF multiwavelets for reducing subspaces of L 2(ℝ n). We characterize scaling sets having three-intervals by dilations 2 and - 2, and discuss joint dilation wavelet sets obtained from these joint dilation scaling sets and also from generalized Journé wavelet sets. Further, we provide a method to obtain joint dilation scaling sets in higher dimensions through scaling sets of lower dimensions and hence obtain multiwavelet sets by dilations A and B. © de Gruyter 2012.