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

Authors
  • LI, Youfa
  • YANG, Shouzhi1, 2
  • 1 College of Mathematics and Information Sciences
  • 2 Department of Mathematics
Type
Published Article
Journal
Acta Mathematica Scientia
Publication Date
Jan 01, 2014
Volume
34
Issue
2
Pages
285–300
Identifiers
DOI: 10.1016/S0252-9602(14)60005-9
Source
Elsevier
Keywords
License
Unknown

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.

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