A class of multiwavelets and projected frames from two-direction wavelets

Abstract

This article aims at studying two-direction refinable functions and two-direction wavelets in the setting ℝs, s > 1. We give a sufficient condition for a two-direction refinable function belonging to L2(ℝs). Then, two theorems are given for constructing biorthogonal (orthogonal) two-direction refinable functions in L2(ℝs) and their biorthogonal (orthogonal) two-direction wavelets, respectively. From the constructed biorthogonal (orthogonal) two-direction wavelets, symmetric biorthogonal (orthogonal) multiwaveles in L2(ℝs can be obtained easily. Applying the projection method to biorthogonal (orthogonal) two-direction wavelets in L2(ℝs, we can get dual (tight) two-direction wavelet frames in L2(ℝm, where. m ≥ s From the projected dual (tight) two-direction wavelet frames in L2(ℝm, symmetric dual (tight) frames in L2(ℝm can be obtained easily. In the end, an example is given to illustrate theoretical results.