A CLASS OF MULTIWAVELETS AND PROJECTED FRAMES FROM TWO-DIRECTION WAVELETS

doi:10.1016/S0252-9602(14)60005-9

Acta mathematica scientia,Series B ›› 2014, Vol. 34 ›› Issue (2): 285-300.doi: 10.1016/S0252-9602(14)60005-9

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A CLASS OF MULTIWAVELETS AND PROJECTED FRAMES FROM TWO-DIRECTION WAVELETS

LI You-Fa, YANG Shou-Zhi*

College of Mathematics and Information Sciences, Guangxi University, Nanning 530004, China；Department of Mathematics, Shantou University, Shantou 515063, China

Received:2011-12-28 Revised:2013-03-14 Online:2014-03-20 Published:2014-03-20
Contact: YANG Shou-Zhi，szyang@stu.edu.cn E-mail:youfalee@hotmail.com；szyang@stu.edu.cn
Supported by:
The first author is supported by the Natural Science Foundation China (11126343) and Guangxi Natural Science Foundation (2013GXNSFBA019010). The second author is supported by Natural Science Foundation China (11071152) and Natural Science Foundation of Guangdong Province (10151503101000025, S2011010004511).

Abstract

Abstract:

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

Key words: Two-direction refinable functions, two-direction wavelets, multiwavelets, wavelet frames, biothogonal (orthogonal), symmetry, projection method

CLC Number:

42C15

LI You-Fa, YANG Shou-Zhi. A CLASS OF MULTIWAVELETS AND PROJECTED FRAMES FROM TWO-DIRECTION WAVELETS[J].Acta mathematica scientia,Series B, 2014, 34(2): 285-300.

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A CLASS OF MULTIWAVELETS AND PROJECTED FRAMES FROM TWO-DIRECTION WAVELETS

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